집합의 연산 연습문제 — Sundstrom, Mathematical Reasoning · 5.3절 · 9a번

Sundstrom, Mathematical Reasoning · 5.3절 · 9a번영어 원문

Let $A$ and $B$ be subsets of some universal set $U$ .

Prove that $A$ and $B - A$ are disjoint sets.

정답·풀이 보기 (영어 원문)

Use a proof by contradiction. Assume the sets are not disjoint and let $x \in A \cap ( B - A )$ . Then $x \in A$ and $x \in B - A$ , which implies that $x \notin A$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 5.3절 · 4a번영어 원문

Let $A$ , $B$ , and $C$ be subsets of some universal set $U$ .

Draw two general Venn diagrams for the sets $A$ , $B$ , and $C$ . On one, shade the region that represents $A - \left( {B \cup C} \right)$ , and on the other, shade the region that represents $\left( {A - B} \right) \cap \left( {A - C} \right)$ . Based on the Venn diagrams, make a conjecture about the relationship between the sets $A - \left( {B \cup C} \right)$ and $\left( {A - B} \right) \cap \left( {A - C} \right)$ .

다 풀었으면 정답 확인

$A - ( {B \cup C} ) = ( {A - B} ) \cap ( {A - C} )$ .

이 문제로 이어서 풀기

# 집합의 연산증명·논술자동 분류