명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 2.4절

Sundstrom, Mathematical Reasoning · 2.4절영어 원문

Write the negation of the statement

$\left( {\forall x \in \mathbb{Z}} \right)\left( {\forall y \in \mathbb{Z}} \right)\left( {x + y = 0} \right)$

in symbolic form and as a sentence written in English.

정답·풀이 보기 (영어 원문)

$\left( {\exists x \in \mathbb{Z}} \right)\left( {\exists y \in \mathbb{Z}} \right)\left( {x + y \ne 0} \right)$ .

There exist integers $x$ and $y$ such that $x + y \ne 0$ .

한 번 더 — 비슷한 문제Sundstrom, 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.

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

다 풀었으면 정답 확인

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.

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