Question

If A and B are any two sets, then $A\cup (A\cap B)$ = ___.

• A. A
• B. B
• C. $A^C$
• D. $B^C$

Answer 1

The correct option is A

A

If A and B are any two sets, then $A\cap B\subseteq A.$ .......(i)

Also, we know $A\subseteq A\cup (A\cap B)$ ......(ii)

from (i) and (ii), we can conclude that
$A\subseteq A\cup (A\cap B)\subseteq A$
$\Rightarrow A\cup (A\cap B)=A$