Elementary set theory z

Question

A ∩ (B ∪C) ⊂ B ∪ (A ∩C)

Can anyone give me a general outline of an approach to take to this proof? I Don't really know where to begin.

score 2 · Accepted Answer · answered Mar 24 '17 at 13:14

2

An elementary approach to such a proof would be to begin by letting $x \in A \cap (B \cup C)$. Then $x \in A$ and $x \in (B \cup C)$ so there are two cases: Either $x \in B \subseteq B \cup (A \cap C)$. Or $x \in C$ and so $x \in A \cap C \subseteq B \cup (A \cap C)$. In both cases we showed $x \in B \cup (A \cap C)$ so we showed any element of $A \cap (B \cup C)$ is contained in $B \cup (A \cap C)$.

answered Mar 24 '17 at 13:14

Oliver Clarke

1,425

Very succinct. Thanks. – Mar 25 '17 at 00:25

score 1 · Answer 2 · answered Mar 24 '17 at 13:04

1

$$A\cap (B\cup C) = (A \cap B)\cup (A\cap C) $$ $$\subset B \cup (A\cap C)$$

answered Mar 24 '17 at 13:04

joeb

2,778

Elementary set theory z

2 Answers2