Bài 3: Các phép toán trên tập hợp
Lý thuyết Các phép toán trên tập hợp
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<h2>1. Hợp và giao của các tập hợp</h2>
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<p style="text-align: left;">Cho hai tập hợp A và B.</p>
<p style="text-align: left;">- Tập hợp các phần tử thuộc A hoặc thuộc B gọi là hợp của hai tập hợp A và B, kí hiệu <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x222A;</mo><mi>B</mi></math>"><span id="MJXc-Node-1" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-2" class="mjx-mrow"><span id="MJXc-Node-3" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-4" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-5" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>∪</mo><mi>B</mi></math></span></span>.</p>
<p style="text-align: left;"><span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x222A;</mo><mi>B</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mo fence="false" stretchy="false">{</mo></mrow></mrow><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi>x</mi><mo>&#x2208;</mo><mi>A</mi></math>"><span id="MJXc-Node-6" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-7" class="mjx-mrow"><span id="MJXc-Node-8" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-9" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-10" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-11" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-12" class="mjx-texatom MJXc-space3"><span id="MJXc-Node-13" class="mjx-mrow"><span id="MJXc-Node-14" class="mjx-texatom"><span id="MJXc-Node-15" class="mjx-mrow"><span id="MJXc-Node-16" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span></span></span></span></span><span id="MJXc-Node-17" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-18" class="mjx-texatom"><span id="MJXc-Node-19" class="mjx-mrow"><span id="MJXc-Node-20" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">|</span></span></span></span><span id="MJXc-Node-21" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-22" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∈</span></span><span id="MJXc-Node-23" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> hoặc <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&#x2208;</mo><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mo fence="false" stretchy="false">}</mo></mrow></mrow></math>"><span id="MJXc-Node-24" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-25" class="mjx-mrow"><span id="MJXc-Node-26" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-27" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∈</span></span><span id="MJXc-Node-28" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-29" class="mjx-texatom"><span id="MJXc-Node-30" class="mjx-mrow"><span id="MJXc-Node-31" class="mjx-texatom"><span id="MJXc-Node-32" class="mjx-mrow"><span id="MJXc-Node-33" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span></span></span></span></span></span></span></p>
<p style="text-align: left;">- Tập hợp các phần tử thuộc cả hai tập hợp A và B gọi là giao của hai tập hợp A và B, kí hiệu <span id="MathJax-Element-4-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x2229;</mo><mi>B</mi></math>"><span id="MJXc-Node-34" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-35" class="mjx-mrow"><span id="MJXc-Node-36" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-37" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-38" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span>.</p>
<p style="text-align: left;"><span id="MathJax-Element-5-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x2229;</mo><mi>B</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mo fence="false" stretchy="false">{</mo></mrow></mrow><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi>x</mi><mo>&#x2208;</mo><mi>A</mi></math>"><span id="MJXc-Node-39" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-40" class="mjx-mrow"><span id="MJXc-Node-41" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-42" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-43" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-44" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-45" class="mjx-texatom MJXc-space3"><span id="MJXc-Node-46" class="mjx-mrow"><span id="MJXc-Node-47" class="mjx-texatom"><span id="MJXc-Node-48" class="mjx-mrow"><span id="MJXc-Node-49" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span></span></span></span></span><span id="MJXc-Node-50" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-51" class="mjx-texatom"><span id="MJXc-Node-52" class="mjx-mrow"><span id="MJXc-Node-53" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">|</span></span></span></span><span id="MJXc-Node-54" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-55" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∈</span></span><span id="MJXc-Node-56" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span>và <span id="MathJax-Element-6-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&#x2208;</mo><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mo fence="false" stretchy="false">}</mo></mrow></mrow></math>"><span id="MJXc-Node-57" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-58" class="mjx-mrow"><span id="MJXc-Node-59" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-60" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∈</span></span><span id="MJXc-Node-61" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-62" class="mjx-texatom"><span id="MJXc-Node-63" class="mjx-mrow"><span id="MJXc-Node-64" class="mjx-texatom"><span id="MJXc-Node-65" class="mjx-mrow"><span id="MJXc-Node-66" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span></span></span></span></span></span></span></p>
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<p><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/15062022/bai-1-trand-32-toan-lop-10-tap-1-D05Alw.png" /></p>
<p><strong>Ví dụ: </strong>Xác định <span id="MathJax-Element-7-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x222A;</mo><mi>B</mi></math>"><span id="MJXc-Node-67" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-68" class="mjx-mrow"><span id="MJXc-Node-69" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-70" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-71" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B </span></span></span></span></span>và <span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x2229;</mo><mi>B</mi></math>"><span id="MJXc-Node-72" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-73" class="mjx-mrow"><span id="MJXc-Node-74" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-75" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-76" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span> trong mỗi trường hợp sau:</p>
<p>a) A= {2; 3; 5; 7}, B={1; 3, 5; 15};</p>
<p>b) <span id="MathJax-Element-9-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mrow><mo>{</mo><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>&#x2208;</mo><mi>R</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi>x</mi><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mrow><mo>}</mo></mrow><mo>,</mo><mi>B</mi><mo>=</mo><mrow><mo>{</mo><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>&#x2208;</mo><mi>R</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mrow class="MJX-TeXAtom-ORD"><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mn>2</mn><mo>=</mo><mn>0</mn></mrow><mo>}</mo></mrow></math>"><span id="MJXc-Node-77" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-78" class="mjx-mrow"><span id="MJXc-Node-79" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-80" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-81" class="mjx-mrow MJXc-space3"><span id="MJXc-Node-82" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span><span id="MJXc-Node-83" class="mjx-texatom"><span id="MJXc-Node-84" class="mjx-mrow"><span id="MJXc-Node-85" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-86" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∈</span></span><span id="MJXc-Node-87" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">R</span></span><span id="MJXc-Node-88" class="mjx-texatom"><span id="MJXc-Node-89" class="mjx-mrow"><span id="MJXc-Node-90" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">|</span></span></span></span><span id="MJXc-Node-91" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-92" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-93" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-94" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-95" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-96" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span><span id="MJXc-Node-97" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-98" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span><span id="MJXc-Node-99" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span><span id="MJXc-Node-100" class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-101" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-102" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-103" class="mjx-mrow MJXc-space3"><span id="MJXc-Node-104" class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R">{</span></span><span id="MJXc-Node-105" class="mjx-texatom"><span id="MJXc-Node-106" class="mjx-mrow"><span id="MJXc-Node-107" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-108" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∈</span></span><span id="MJXc-Node-109" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">R</span></span><span id="MJXc-Node-110" class="mjx-texatom"><span id="MJXc-Node-111" class="mjx-mrow"><span id="MJXc-Node-112" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">|</span></span></span></span><span id="MJXc-Node-113" class="mjx-texatom"><span id="MJXc-Node-114" class="mjx-mrow"><span id="MJXc-Node-115" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-116" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sup><span class="mjx-sup"><span id="MJXc-Node-117" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span></span></sup></span></span></span><span id="MJXc-Node-118" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-119" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-120" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-121" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span><span id="MJXc-Node-122" class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R">}</span></span></span></span></span></span></p>
<p>c) A là tập hợp các hình bình hành, B là tập hợp các hình thoi.</p>
<p><em><strong>Giải</strong></em></p>
<p>a) 4<span id="MathJax-Element-10-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x222A;</mo><mi>B</mi></math>"><span id="MJXc-Node-123" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-124" class="mjx-mrow"><span id="MJXc-Node-125" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-126" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-127" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span> = (1;2;3;5; 7; 15), <span id="MathJax-Element-11-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x2229;</mo><mi>B</mi></math>"><span id="MJXc-Node-128" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-129" class="mjx-mrow"><span id="MJXc-Node-130" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-131" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-132" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span>= (3; 5}</p>
<p>b) Phương trình x(x + 2) = 0 có hai nghiệm là 0 và -2. nên A = {-2; 0}</p>
<p>Phương trình <span id="MathJax-Element-12-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mn>2</mn><mo>=</mo><mn>0</mn></math>"><span id="MJXc-Node-133" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-134" class="mjx-mrow"><span id="MJXc-Node-135" class="mjx-texatom"><span id="MJXc-Node-136" class="mjx-mrow"><span id="MJXc-Node-137" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-138" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><span class="mjx-sup"><span id="MJXc-Node-139" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span></span></span></span></span><span id="MJXc-Node-140" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-141" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-142" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-143" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mn>2</mn><mo>=</mo><mn>0</mn></math></span></span> vô nghiệm, nên B = Ø</p>
<p>Từ đó <span id="MathJax-Element-13-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x222A;</mo><mi>B</mi><mo>=</mo><mi>A</mi><mo>&#x222A;</mo><mi mathvariant="normal">&#x2205;</mi><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"></mrow></mrow><mo>=</mo><mi>A</mi><mo>=</mo><mrow><mo>{</mo><mrow class="MJX-TeXAtom-ORD"><mo>&#x2212;</mo><mn>2</mn><mo>;</mo><mn>0</mn></mrow><mo>}</mo></mrow><mo>,</mo><mi>A</mi><mo>&#x2229;</mo><mi>B</mi><mo>=</mo><mi>A</mi><mo>&#x2229;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"></mrow></mrow><mi mathvariant="normal">&#x2205;</mi><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"></mrow></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"></mrow></mrow><mi mathvariant="normal">&#x2205;</mi><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"></mrow></mrow></math>"><span id="MJXc-Node-144" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-145" class="mjx-mrow"><span id="MJXc-Node-146" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-147" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-148" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-149" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-150" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-151" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-152" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∅</span></span><span id="MJXc-Node-153" class="mjx-texatom"><span id="MJXc-Node-154" class="mjx-mrow"><span id="MJXc-Node-155" class="mjx-texatom"><span id="MJXc-Node-156" class="mjx-mrow"></span></span></span></span><span id="MJXc-Node-157" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-158" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-159" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-160" class="mjx-mrow MJXc-space3"><span id="MJXc-Node-161" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span><span id="MJXc-Node-162" class="mjx-texatom"><span id="MJXc-Node-163" class="mjx-mrow"><span id="MJXc-Node-164" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-165" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-166" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-167" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span><span id="MJXc-Node-168" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span><span id="MJXc-Node-169" class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-170" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-171" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-172" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-173" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-174" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-175" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-176" class="mjx-texatom MJXc-space2"><span id="MJXc-Node-177" class="mjx-mrow"><span id="MJXc-Node-178" class="mjx-texatom"><span id="MJXc-Node-179" class="mjx-mrow"></span></span></span></span><span id="MJXc-Node-180" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∅</span></span><span id="MJXc-Node-181" class="mjx-texatom"><span id="MJXc-Node-182" class="mjx-mrow"><span id="MJXc-Node-183" class="mjx-texatom"><span id="MJXc-Node-184" class="mjx-mrow"></span></span></span></span><span id="MJXc-Node-185" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-186" class="mjx-texatom MJXc-space3"><span id="MJXc-Node-187" class="mjx-mrow"><span id="MJXc-Node-188" class="mjx-texatom"><span id="MJXc-Node-189" class="mjx-mrow"></span></span></span></span><span id="MJXc-Node-190" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∅</span></span></span></span></span></p>
<p>e) Vì mỗi hình thoi cũng là hình bình hành nên <span id="MathJax-Element-14-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>&#x2282;</mo><mi>A</mi></math>"><span id="MJXc-Node-195" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-196" class="mjx-mrow"><span id="MJXc-Node-197" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-198" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">⊂</span></span><span id="MJXc-Node-199" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span>. Từ đó, <span id="MathJax-Element-15-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x222A;</mo><mi>B</mi><mo>=</mo><mi>A</mi><mo>,</mo><mi>A</mi><mo>&#x2229;</mo><mi>B</mi><mo>=</mo><mi>B</mi></math>"><span id="MJXc-Node-200" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-201" class="mjx-mrow"><span id="MJXc-Node-202" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-203" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-204" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-205" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-206" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-207" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-208" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-209" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-210" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-211" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-212" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span></p>
<p><em><strong>Nhận xét:</strong></em></p>
<ul>
<li>Nếu A và B là hai tập hợp hữu hạn thì <span id="MathJax-Element-16-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mi>A</mi><mo>&#x222A;</mo><mi>B</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>n</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mo>+</mo><mi>n</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>&#x2212;</mo><mi>n</mi><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mi>A</mi><mo>&#x2229;</mo><mi>B</mi></mrow><mo>)</mo></mrow></math>"><span id="MJXc-Node-213" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-214" class="mjx-mrow"><span id="MJXc-Node-215" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">n</span></span><span id="MJXc-Node-216" class="mjx-mrow MJXc-space1"><span id="MJXc-Node-217" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-218" class="mjx-texatom"><span id="MJXc-Node-219" class="mjx-mrow"><span id="MJXc-Node-220" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-221" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-222" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span><span id="MJXc-Node-223" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span><span id="MJXc-Node-224" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-225" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">n</span></span><span id="MJXc-Node-226" class="mjx-mrow MJXc-space1"><span id="MJXc-Node-227" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-228" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-229" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span><span id="MJXc-Node-230" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-231" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">n</span></span><span id="MJXc-Node-232" class="mjx-mrow MJXc-space1"><span id="MJXc-Node-233" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-234" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-235" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span><span id="MJXc-Node-236" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-237" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">n</span></span><span id="MJXc-Node-238" class="mjx-mrow MJXc-space1"><span id="MJXc-Node-239" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-240" class="mjx-texatom"><span id="MJXc-Node-241" class="mjx-mrow"><span id="MJXc-Node-242" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-243" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-244" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span><span id="MJXc-Node-245" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span></span></li>
<li>Đặc biệt, nếu A và B không có phần tử chung, tức <span id="MathJax-Element-17-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#x2229;</mo><mi>B</mi><mo>=</mo><mi mathvariant="normal">&#x2205;</mi></math>"><span id="MJXc-Node-246" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-247" class="mjx-mrow"><span id="MJXc-Node-248" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-249" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∩</span></span><span id="MJXc-Node-250" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-251" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-252" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∅</span></span></span></span></span> thì <span id="MathJax-Element-18-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mi>A</mi><mo>&#x222A;</mo><mi>B</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>n</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mo>+</mo><mi>n</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></math>"><span id="MJXc-Node-253" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-254" class="mjx-mrow"><span id="MJXc-Node-255" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">n</span></span><span id="MJXc-Node-256" class="mjx-mrow MJXc-space1"><span id="MJXc-Node-257" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-258" class="mjx-texatom"><span id="MJXc-Node-259" class="mjx-mrow"><span id="MJXc-Node-260" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-261" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">∪</span></span><span id="MJXc-Node-262" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span><span id="MJXc-Node-263" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span><span id="MJXc-Node-264" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-265" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">n</span></span><span id="MJXc-Node-266" class="mjx-mrow MJXc-space1"><span id="MJXc-Node-267" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-268" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-269" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span><span id="MJXc-Node-270" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-271" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">n</span></span><span id="MJXc-Node-272" class="mjx-mrow MJXc-space1"><span id="MJXc-Node-273" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-274" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-275" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span></span></li>
</ul>
<div id="12">
<h2>2. Hiệu của hai tập hợp, phần bù của tập con</h2>
</div>
<table border="1" cellspacing="1" cellpadding="1">
<thead>
<tr>
<th scope="row">
<p>Cho hai tập hợp A và B.</p>
<p>- Tâp hợp các phần tử thuộc A nhưng không thuộc B gọi là liệu của A và B, kí hiệu <span id="MathJax-Element-19-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi class="MJX-variant" mathvariant="normal">&#x2216;</mi><mi>B</mi></math>"><span id="MJXc-Node-276" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-277" class="mjx-mrow"><span id="MJXc-Node-278" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-279" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∖</span></span><span id="MJXc-Node-280" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span></p>
<p><span id="MathJax-Element-20-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi class="MJX-variant" mathvariant="normal">&#x2216;</mi><mi>B</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mo fence="false" stretchy="false">{</mo></mrow></mrow><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi>x</mi><mo>&#x2208;</mo><mi>A</mi></math>"><span id="MJXc-Node-281" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-282" class="mjx-mrow"><span id="MJXc-Node-283" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-284" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∖</span></span><span id="MJXc-Node-285" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-286" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-287" class="mjx-texatom MJXc-space3"><span id="MJXc-Node-288" class="mjx-mrow"><span id="MJXc-Node-289" class="mjx-texatom"><span id="MJXc-Node-290" class="mjx-mrow"><span id="MJXc-Node-291" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span></span></span></span></span><span id="MJXc-Node-292" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-293" class="mjx-texatom"><span id="MJXc-Node-294" class="mjx-mrow"><span id="MJXc-Node-295" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">|</span></span></span></span><span id="MJXc-Node-296" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-297" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∈</span></span><span id="MJXc-Node-298" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> và <span id="MathJax-Element-21-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&#x2209;</mo><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mo fence="false" stretchy="false">}</mo></mrow></mrow></math>"><span id="MJXc-Node-299" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-300" class="mjx-mrow"><span id="MJXc-Node-301" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-302" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">∉</span></span><span id="MJXc-Node-303" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-304" class="mjx-texatom"><span id="MJXc-Node-305" class="mjx-mrow"><span id="MJXc-Node-306" class="mjx-texatom"><span id="MJXc-Node-307" class="mjx-mrow"><span id="MJXc-Node-308" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span></span></span></span></span></span></span>.</p>
<p>- Nếu A là tập con của E thì hiệu <span id="MathJax-Element-22-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi class="MJX-variant" mathvariant="normal">&#x2216;</mi><mi>A</mi></math>"><span id="MJXc-Node-309" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-310" class="mjx-mrow"><span id="MJXc-Node-311" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-312" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∖</span></span><span id="MJXc-Node-313" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> gọi là phân bù của A trong E, kí hiệu <span id="MathJax-Element-23-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msub><mi>C</mi><mi>E</mi></msub></mrow><mi>A</mi></math>"><span id="MJXc-Node-314" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-315" class="mjx-mrow"><span id="MJXc-Node-316" class="mjx-texatom"><span id="MJXc-Node-317" class="mjx-mrow"><span id="MJXc-Node-318" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-319" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-320" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></sub></span></span></span><span id="MJXc-Node-321" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span>.</p>
</th>
</tr>
</thead>
</table>
<p><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/15062022/bai-1-trand-39-toan-lop-10-tap-1-3-a94xVb.png" /></p>
<p><strong>Ví dụ: </strong>Cho E = {x <span id="MathJax-Element-24-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2208;</mo></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∈</mo></math></span></span> N | x < 10}, A = {0; 2' 4; 6; 8}, B = {0; 3; 6; 9}</p>
<p>Xác định các tập hợp <span id="MathJax-Element-25-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi class="MJX-variant" mathvariant="normal">&#x2216;</mi><mi>B</mi><mo>,</mo><mi>B</mi><mi class="MJX-variant" mathvariant="normal">&#x2216;</mi><mi>A</mi><mo>,</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>C</mi><mi>E</mi></msub></mrow><mi>A</mi><mo>,</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>C</mi><mi>E</mi></msub></mrow><mi>B</mi></math>"><span id="MJXc-Node-325" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-326" class="mjx-mrow"><span id="MJXc-Node-327" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-328" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∖</span></span><span id="MJXc-Node-329" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-330" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-331" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-332" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∖</span></span><span id="MJXc-Node-333" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-334" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-335" class="mjx-texatom MJXc-space1"><span id="MJXc-Node-336" class="mjx-mrow"><span id="MJXc-Node-337" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-338" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-339" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></sub></span></span></span><span id="MJXc-Node-340" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-341" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-342" class="mjx-texatom MJXc-space1"><span id="MJXc-Node-343" class="mjx-mrow"><span id="MJXc-Node-344" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-345" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-346" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></sub></span></span></span><span id="MJXc-Node-347" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span></p>
<p><strong>Giải:</strong></p>
<p>Ta có: <span id="MathJax-Element-26-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; overflow-wrap: normal; word-break: break-word; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi class="MJX-variant" mathvariant="normal">&#x2216;</mi><mi>B</mi><mo>=</mo><mrow><mo>{</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mo>;</mo><mn>4</mn><mo>;</mo><mn>8</mn></mrow><mo>}</mo></mrow><mo>,</mo><mi>B</mi><mi class="MJX-variant" mathvariant="normal">&#x2216;</mi><mi>A</mi><mo>=</mo><mrow><mo>{</mo><mrow class="MJX-TeXAtom-ORD"><mn>3</mn><mo>;</mo><mn>9</mn></mrow><mo>}</mo></mrow><mo>,</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>C</mi><mi>E</mi></msub></mrow><mi>A</mi><mo>=</mo><mrow><mo>{</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mo>;</mo><mn>3</mn><mo>;</mo><mn>5</mn><mo>;</mo><mn>7</mn><mo>;</mo><mn>9</mn></mrow><mo>}</mo></mrow><mo>,</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>C</mi><mi>E</mi></msub></mrow><mi>B</mi><mo>=</mo><mrow><mo>{</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mo>;</mo><mn>2</mn><mo>;</mo><mn>4</mn><mo>;</mo><mn>5</mn><mo>;</mo><mn>7</mn><mo>;</mo><mn>8</mn></mrow><mo>}</mo></mrow></math>"><span id="MJXc-Node-348" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-349" class="mjx-mrow"><span id="MJXc-Node-350" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-351" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∖</span></span><span id="MJXc-Node-352" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-353" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-354" class="mjx-mrow MJXc-space3"><span id="MJXc-Node-355" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span><span id="MJXc-Node-356" class="mjx-texatom"><span id="MJXc-Node-357" class="mjx-mrow"><span id="MJXc-Node-358" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-359" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-360" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">4</span></span><span id="MJXc-Node-361" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-362" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">8</span></span></span></span><span id="MJXc-Node-363" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span><span id="MJXc-Node-364" class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">, </span></span><span id="MJXc-Node-365" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-366" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">∖</span></span><span id="MJXc-Node-367" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-368" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-369" class="mjx-mrow MJXc-space3"><span id="MJXc-Node-370" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span><span id="MJXc-Node-371" class="mjx-texatom"><span id="MJXc-Node-372" class="mjx-mrow"><span id="MJXc-Node-373" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">3</span></span><span id="MJXc-Node-374" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-375" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">9</span></span></span></span><span id="MJXc-Node-376" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span><span id="MJXc-Node-377" class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">, </span></span><span id="MJXc-Node-378" class="mjx-texatom MJXc-space1"><span id="MJXc-Node-379" class="mjx-mrow"><span id="MJXc-Node-380" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-381" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-382" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></sub></span></span></span><span id="MJXc-Node-383" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-384" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-385" class="mjx-mrow MJXc-space3"><span id="MJXc-Node-386" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span><span id="MJXc-Node-387" class="mjx-texatom"><span id="MJXc-Node-388" class="mjx-mrow"><span id="MJXc-Node-389" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">1</span></span><span id="MJXc-Node-390" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-391" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">3</span></span><span id="MJXc-Node-392" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-393" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-394" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-395" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">7</span></span><span id="MJXc-Node-396" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-397" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">9</span></span></span></span><span id="MJXc-Node-398" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span><span id="MJXc-Node-399" class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">, </span></span><span id="MJXc-Node-400" class="mjx-texatom MJXc-space1"><span id="MJXc-Node-401" class="mjx-mrow"><span id="MJXc-Node-402" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-403" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-404" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></sub></span></span></span><span id="MJXc-Node-405" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-406" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-407" class="mjx-mrow MJXc-space3"><span id="MJXc-Node-408" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">{</span></span><span id="MJXc-Node-409" class="mjx-texatom"><span id="MJXc-Node-410" class="mjx-mrow"><span id="MJXc-Node-411" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">1</span></span><span id="MJXc-Node-412" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-413" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-414" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-415" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">4</span></span><span id="MJXc-Node-416" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-417" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-418" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-419" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">7</span></span><span id="MJXc-Node-420" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-421" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">8</span></span></span></span><span id="MJXc-Node-422" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">}</span></span></span></span></span></span></p>
<p><strong>Chú ý: </strong>Trong các chương sau, để tìm các tập hợp là hợp, giao, hiệu, phần bù của những tập con của tập số thực, ta thường vẽ sơ đồ trên trục số.</p>
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