Question

If $A=$ {$1,2,3$}, $B=$ {$2,4$} and $C=$ {$1,2$}, then prove $(A\cup B)\cup C=A\cup (B\cup C)$

Answer 1

Given, $A=$ {$1,2,3$}, $B=$ {$2,4$} and $C=$ {$1,2$}
First take L.H.S $(A\cup B)\cup C$
$(A\cup B)=1,2,3,4$
$(A\cup B)\cup C$ $=$ {$1,2,3,4$}
Similarly, take R.H.S $A\cup (B\cup C)$
$B\cup C$ $=$ {$1,2,4$}
$A\cup (B\cup C)$ $=$ {$1,2,3,4$}
So, L.H.S $=$ R.H.S
Hence, proved.