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

Sundstrom, Mathematical Reasoning · 2.4절 · 6a번영어 원문

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

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

.

.

Explain why this sentence is an open sentence and not a statement.

정답·풀이 보기 (영어 원문)

It is not a statement since $x$ is an unquantified variable.

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

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

$\left(\exists x \in \mathbb{Q} \right) \left( x^2 - 3x - 7 = 0 \right)$ .

다 풀었으면 정답 확인

There exists a rational number $x$ such that $x^2 - 3x - 7 = 0$ . This statement is false since the solutions of the equation are $x = \dfrac{3 \pm \sqrt{37}}{2}$ , which are irrational numbers.

이 문제로 이어서 풀기

# 명제와 조건계산자동 분류