Question

Let $A$ and $B$ be two sets such that $A\cap B=\varphi$. Find the value of $(A\cup B^{\prime })=$

• A. $A^{\prime }$
• B. $B$
• C. $\varphi$
• D. none of these

Answer 1

The correct option is B $B$

Given, $A\cap B=\varphi$.

Now,

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

$=(A^{\prime }\cap B{)}^{\prime }$ [ Using De Morgan's law]

$=B^{\prime }$. [ As $A^{\prime }\cap B=B-(A\cap B)=B$ since $A\cap B=\varphi$]