Question

If $A=$ {$0,3,5$}, $B=$ {$1,5$} and $C=$ {$7,2$}, then prove $(A\cap B)\cap C=A\cap (B\cap C)$

Answer 1

Given, $A=$ {$0,3,5$}, $B=$ {$1,5$} and $C=$ {$7,2$}
First take L.H.S $(A\cap B)\cap C$
$(A\cap B)=5$
$(A\cap B)\cap C$ $=$ {}
Similarly, take R.H.S $A\cap (B\cap C)$
$B\cap C$ $=$ {}
$A\cap (B\cap C)$ $=$ {}
So, L.H.S $=$ R.H.S
Hence, proved.