명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 2.4절 · 1b번

Sundstrom, Mathematical Reasoning · 2.4절 · 1b번영어 원문

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

$\left( \exists x \in \mathbb{R} \right) \left( x^2 + 1 = 0 \right)$ .

정답·풀이 보기 (영어 원문)

There exists a real number $x$ such that $x^2 + 1 = 0$ . This statement is false since the only solutions of the equation are $i$ and $-i$ , which are not real numbers.

한 번 더 — 비슷한 문제Sundstrom, 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?

다 풀었으면 정답 확인

It is a false statement.

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