Question

${[B^{\prime }\cup (B^{\prime }-A\left)\right]}^{\prime }$ =

• A. A
• B. B
• C. A - B
• D. B - A

Answer 1

The correct option is B B

${[B^{\prime }\cup (B^{\prime }-A\left)\right]}^{\prime }={[B^{\prime }\cup (B^{\prime }\cap A^{\prime }\left)\right]}^{\prime }(\because A-B=A\cap B^{\prime })={\left[\right(B^{\prime }\cup B^{\prime })\cap (B^{\prime }\cup A^{\prime }\left)\right]}^{\prime }\left[\text{Distributive property}\right]={[B^{\prime }\cap (B\cap A{)}^{\prime }]}^{\prime }\left[\text{de-Morgan's law for intersection}\right]={\left(B^{\prime }\right)}^{\prime }\cup \left(\right(B\cap A{)}^{\prime }{)}^{\prime }(\because {(B\cap B)}^{\prime }=A^{\prime }\cup B^{\prime })=B\cup (B\cap A)=B$