Question

If $A=\{2,3,4,8,10\}$, $B=\{3,4,5,10,12\}$ and $C=\{4,5,6,12,14\}$
Find $(A\cup B)\cap (A\cup C)$ and $(A\cap B)\cup (A\cap C)$

Answer 1

(i) $A\cup (B\cap C)=\{2,3,4,8,10\}\cup \{4,5,12\}$
$=\{2,3,4,5,8,10,12\}$
(ii) $A\cap (B\cup C)=\{2,3,4,8,10\}\cap \{3,4,5,6,10,12,14\}$
$=\{3,4,10\}$