Question

For any two sets $A$ and $B,$ if $(A\cup B{)}^{\prime }=A^{\prime }\cup B^{\prime },$ then

• A. $A\subseteq B$
• B. $B\subseteq A$
• C. $A^{\prime }=B$
• D. $A=B$

Answer 1

The correct option is D $A=B$

Given that $(A\cup B{)}^{\prime }=A^{\prime }\cup B^{\prime }$
By De Morgan's law,
$(A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }$
So, $A^{\prime }\cap B^{\prime }=A^{\prime }\cup B^{\prime }$
This is possible only if $A=B$ $(\because P\cup Q=P\cap Q\Rightarrow P=Q)$