집합의 뜻과 포함 관계 연습문제 — Sundstrom, Mathematical Reasoning · 5.2절 · 1a번

Sundstrom, Mathematical Reasoning · 5.2절 · 1a번영어 원문

Let $A = \left\{ {\left. {x \in \mathbb{R}} \right| x^2 \lt 4} \right\}$ and let $B = \left\{ {x \in \mathbb{R}\left. \right| x \lt 2} \right\}$ .

Is $A \subseteq B$ ? Justify your conclusion with a proof or a counterexample.

정답·풀이 보기 (영어 원문)

The set $A$ is a subset of $B$ . To prove this, we let $x \in A$ . Then $- 2 \lt x \lt 2$ . Since $x \lt 2$ , we conclude that $x \in B$ and hence, we have proved that $A$ is a subset of $B$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 5.2절 · 1b번영어 원문

Let $A = \left\{ {\left. {x \in \mathbb{R}} \right| x^2 \lt 4} \right\}$ and let $B = \left\{ {x \in \mathbb{R}\left. \right| x \lt 2} \right\}$ .

Is $B \subseteq A$ ? Justify your conclusion with a proof or a counterexample.

다 풀었으면 정답 확인

The set $B$ is not a subset of $A$ . There are many examples of a real number that is in $B$ but not in $A$ . For example, $-3$ is in $A$ , but $-3$ is not in $B$ .

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