집합의 뜻과 포함 관계 연습문제 — Sundstrom, Mathematical Reasoning · 5.1절 · 3e번

Sundstrom, Mathematical Reasoning · 5.1절 · 3e번영어 원문

Assume that the universal set is the set of integers. Let

$\begin{aligned}A & = \left\{ { - 3, - 2,2,3} \right\}\!, & B & = \left\{ {x \in \mathbb{Z}\left. \right|x^2 \leq 9} \right\}\!, \\ C & = \left\{ {\left. {x \in \mathbb{Z}} \right|x \geq - 3} \right\}\!, & D & = \left\{ {1,2,3,4} \right\}\!\end{aligned}$

. In each of the following, fill in the blank with one or more of the symbols $\subset$ , $\subseteq$ , $\not \subseteq$ , $=$ , $\ne$ , $\in$ , $\text{ or } \notin$ so that the resulting statement is true. For each blank, include all symbols that result in a true statement. If none of these symbols makes a true statement, write nothing in the blank.

4_____ $B$

정답·풀이 보기 (영어 원문)

$4 \not \in B$

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.3절 · 2b번영어 원문

Each of the following sets is defined using the roster method.

$\begin{aligned}A & = \left\{1, 4, 9, 16, 25, \ldots \right\} & B & = \left\{\ldots, -\pi^4, -\pi^3, -\pi^2, -\pi, -1 \right\} \\ C & = \left\{3, 9, 15, 21, 27, \ldots \right\} & D & = \left\{0, 4, 8, \ldots, 96, 100 \right\}\end{aligned}$

Use set builder notation to describe each set.

다 풀었으면 정답 확인

Possible answers:

$\begin{aligned}A & = \left\{ n^2 \mid n \in \mathbb{N} \right\} \\ B & = \left\{ -\pi^n \mid n \text{ ~is a nonnegative integer } \right\} \\ C & = \left\{ 6n + 3 \mid n \text{ ~is a nonnegative integer } \right\} = \left\{6n - 3 \mid n \in \mathbb{N} \right\} \\ D & = \left\{ 4n \mid n \in \mathbb{Z} \text{ ~and~ } 0 \leq n \leq 25 \right\}\end{aligned}$

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# 집합의 뜻과 포함 관계계산자동 분류