명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 2.4절 · 3c번

Sundstrom, Mathematical Reasoning · 2.4절 · 3c번영어 원문

For each of the following statements

Write the statement as an English sentence that does not use the symbols for quantifiers. - Write the negation of the statement in symbolic form in which the negation symbol is not used. - Write a useful negation of the statement in an English sentence that does not use the symbols for quantifiers.

$\left( {\forall x \in \mathbb{Z}} \right)\left( {x\text{ is even or } x\text{ is odd } } \right)$ .

정답·풀이 보기 (영어 원문)

For each integer $x$ , $x$ is even or $x$ is odd. The negation is $\left( \exists x \in \mathbb{Z} \right) \left( x \text{ is odd and $x$ is even } \right)$ , which is, There exists an integer $x$ such that $x$ is odd and $x$ is even.

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.4절 · 3h번영어 원문

For each of the following statements

Write the statement as an English sentence that does not use the symbols for quantifiers. - Write the negation of the statement in symbolic form in which the negation symbol is not used. - Write a useful negation of the statement in an English sentence that does not use the symbols for quantifiers.

$\left( {\exists x \in \mathbb{R}} \right) \left( {\cos ( {2x} ) = 2( {\cos x} )} \right)$ .

다 풀었으면 정답 확인

There exists a real number $x$ such that $\cos \left( 2x \right) = 2 \left( \cos x \right)$ . The negation is $\left( {\forall x \in \mathbb{R}} \right) \left( \cos \left( 2x \right) \ne 2 \left( \cos x \right) \right)$ , which is, For each real number $x$ , $\cos \left( 2x \right) \ne 2 \left( \cos x \right)$ .

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