Question

If A and B are two given sets, then $A\cap (A\cap B{)}^{\prime }$ is equal to

• A. A
• B. $(A\cap B^{\prime })$
• C. ∅
• D. B

Answer 1

The correct option is B

$(A\cap B^{\prime })$

$A\cap (A\cap B{)}^{\prime }=A\cap (A^{\prime }\cup B^{\prime }$) [$\because (A\cap B{)}^{\prime }=A^{\prime }\cup B^{\prime }$ by De Morgans law ]

$=(A\cap A^{\prime })\cup (A\cap B^{\prime }$)

$=\varnothing \cup (A\cap B^{\prime })=(A\cap B^{\prime })....\left(\right(A\cap A^{\prime })=\varnothing$)