Hướng dẫn Giải Thực hành 8 (Trang 14, SGK Toán 10 - Bộ Chân Trời Sáng Tạo mới nhất)

Thực hành 8 (Trang 14, SGK Toán 10, Tập 1 - Bộ Chân Trời Sáng Tạo mới nhất)

Thực hành 8 (Trang 14, SGK Toán 10, Bộ Chân Trời Sáng Tạo mới nhất, Tập 1) Xét tính đúng sai và viết mệnh đề phủ định của các mệnh đề sau: a) <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>">∀x∈<span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℝ</mi></math>, x2>0; b) <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>5</mn><mi>x</mi><mo>&#x2212;</mo><mn>4</mn><mo>;</mo></math>">∃x∈<span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℝ</mi></math>,x2=5x−4; c) <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x2124;</mi><mo>,</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0.</mn></math>">∃x∈<span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x2124;</mi><mo>,</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0.</mn></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℤ</mi></math>,2x+1=0.   Hướng dẫn giải a) Gọi: P: “<span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>">∀x ∈ <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℝ</mi></math>, x2>0”. Chọn x = 0 ∈ ℝ, ta thấy x2 = 02 = 0 > 0 (vô lí). Do đó mệnh đề P sai. Mệnh đề phủ định của mệnh đề P là  <math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>P</mi></menclose></math>: “<span id="MathJax-Element-5-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>P</mi><mo>&#xAF;</mo></mover><mo>:</mo><mo>&quot;</mo><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&#x2264;</mo><mn>0</mn><mo>&quot;</mo></math>"><span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>5</mn><mi>x</mi><mo>&#x2212;</mo><mn>4</mn><mo>;</mo></math>">∃<span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>">x ∈ <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℝ</mi></math>, x2>0”.   b) Gọi Q: “<span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>5</mn><mi>x</mi><mo>&#x2212;</mo><mn>4</mn><mo>;</mo></math>">∃x∈<span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℝ</mi></math>, x2=5x−4”. Xét phương trình: x2 = 5x – 4  ⇔ x2 – 5x + 4 = 0  <mo><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo> </mo><mi>h</mi><mi>o</mi><mi>ặ</mi><mi>c</mi><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn> Ta thấy hai nghiệm 1 và 4 đều là các số thực. Do đó mệnh đề Q đúng. Mệnh đề phủ định của mệnh đề Q là: <math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>Q</mi></menclose></math> = “<span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>Q</mi><mo>&#xAF;</mo></mover><mo>:</mo><mo>&quot;</mo><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&#x2260;</mo><mn>5</mn><mi>x</mi><mo>&#x2212;</mo><mn>4</mn><mo>&quot;</mo></math>">∀<span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>5</mn><mi>x</mi><mo>&#x2212;</mo><mn>4</mn><mo>;</mo></math>">x ∈ <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x211D;</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn><mo>;</mo></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℝ</mi></math>, x2=5x−4”.   c) Gọi H: “<span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x2124;</mi><mo>,</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0.</mn></math>">∃x ∈ <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2203;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x2124;</mi><mo>,</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0.</mn></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℤ</mi></math>, 2x+1=0”. Xét 2x + 1 = 0  <span id="MathJax-Element-10-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x21D4;</mo><mi>x</mi><mo>=</mo><mo>&#x2212;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>&#x2209;</mo><mi>&#x2124;</mi></math>">⇔ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2 </mn></mfrac></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn></mn></mfrac><mo>∉ </mo><mi>ℤ</mi></math> Do đó không tồn tại giá trị nguyên nào của x để 2x + 1 = 0. Vì vậy mệnh đề H là mệnh đề sai. Mệnh đề phủ định của mệnh đề H là: <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>H</mi><mo>¯</mo></mover></math>: “<span id="MathJax-Element-11-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>H</mi><mo>&#xAF;</mo></mover><mo>:</mo><mo>&quot;</mo><mo>&#x2200;</mo><mi>x</mi><mo>&#x2208;</mo><mi>&#x2124;</mi><mo>,</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>&#x2260;</mo><mn>0</mn><mo>&quot;</mo></math>">∀x ∈ <span id="MathJax-Element-10-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: 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; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x21D4;</mo><mi>x</mi><mo>=</mo><mo>&#x2212;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>&#x2209;</mo><mi>&#x2124;</mi></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ℤ</mi></math>, 2x+1≠0”.

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