명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 2.4절 · 6c번

Sundstrom, Mathematical Reasoning · 2.4절 · 6c번영어 원문

Assume that the universal set is $\mathbb{Z}$ . Consider the following sentence:

$\left( {\exists t \in \mathbb{Z}} \right)\left( {t \cdot x = 20} \right)$

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If 8 is substituted for $x$ , is the resulting sentence a statement? If it is a statement, is the statement true or false?

정답·풀이 보기 (영어 원문)

It is a false statement.

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.4절 · 1c번영어 원문

For each of the following, write the statement as an English sentence and then explain why the statement is false.

$\left( \exists m \in \mathbb{N} \right) \left( m^2 \lt 1 \right)$ .

다 풀었으면 정답 확인

There exists a natural number $m$ such that $m^2 \lt 1$ . This statement is false because if $m$ is a natural number, then $m \geq 1$ and hence, $m^2 \geq 1$ .

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