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

Sundstrom, Mathematical Reasoning · 2.4절 · 3e번영어 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.

$\left( {\forall x \in \mathbb{Z}} \right)\left( {\text{ If } x^2 \text{ is odd, then } x\text{ is odd } } \right)$ .

정답·풀이 보기 (영어 원문)

For each integer $x$ , if $x^2$ is odd, then $x$ is odd. The negation is $\left( \exists x \in \mathbb{Z} \right) \left( x^2 \text{ is odd and $x$ is even } \right)$ , which is, There exists an integer $x$ such that $x^2$ is odd and $x$ is even.

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.4절 · 3a번영어 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.

$\left( {\exists x \in \mathbb{Q}} \right)\left( {x > \sqrt 2 } \right)$ .

다 풀었으면 정답 확인

There exists a rational number $x$ such that $x > \sqrt{2}$ . The negation is $\left( {\forall x \in \mathbb{Q}} \right) \left( {x \leq \sqrt 2 } \right)$ , which is, For each rational number $x$ , $x \le \sqrt{2}$ .

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