Question

Using properties of sets, show that

(i) $A\cup (A\cap B)=A$ (ii) $A\cap (A\cup B)=A.$

Answer 1

(i) We know that if $A\subset B$ then

$A\cap B=B$

Also $A\cap B\subset A$

$\therefore A\cup (A\cap B)=A.$

(ii) We know that if $A\subset B$ then

$A\cap B=A$

Also $A\subset A\cup B$

$\therefore A\cap (A\cup B)=A.$