Question

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

Answer 1

Given $A=\{2,3,4,8,10\}$, $B=\{3,4,5,10,12\}$ and $C=\{4,5,6,12,14\}$

1) $A\cup B=\{2,3,4,8,10\}\cup \{3,4,5,10,12\}$

$\therefore A\cup B=\{2,3,4,5,8,10,12\}$

2) $A\cup C=\{2,3,4,8,10\}\cup \{4,5,6,12,14\}$

$\therefore A\cup C=\{2,3,4,5,6,8,10,12,14\}$

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

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

$\therefore n(A\cup B)\cap (A\cup C)=7$