집합의 뜻과 포함 관계 연습문제 — Sundstrom, Mathematical Reasoning · 5.2절

Sundstrom, Mathematical Reasoning · 5.2절영어 원문

Let $A = \left\{ x \in \mathbb{Z} \mid x \text{ is a multiple of 9 } \right\}$ and let $B = \left\{ x \in \mathbb{Z} \mid x \text{ is a multiple of 3 } \right\}$ .

Is the set $A$ a subset of $B$ ? Justify your conclusion.

정답·풀이 보기 (영어 원문)

The set $A$ is a subset of $B$ . To prove this, we let $x \in A$ . Then there exists an integer $m$ such that $x = 9m$ , which can be written as

$x = 3 \left( 3m \right)\!$

. Since $3m \in \mathbb{Z}$ , the last equation proves that $x$ is a multiple of 3 and so $x \in B$ . Therefore, $A \subseteq B$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 5.2절영어 원문

Let $A = \left\{ x \in \mathbb{Z} \mid x \text{ is a multiple of 9 } \right\}$ and let $B = \left\{ x \in \mathbb{Z} \mid x \text{ is a multiple of 3 } \right\}$ .

Is the set $A$ equal to the set $B$ ? Justify your conclusion.

다 풀었으면 정답 확인

The set $A$ is not equal to the set $B$ . We note that $3 \in B$ but $3 \notin A$ . Therefore, $B \not \subseteq A$ and, hence, $A \ne B$ .

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