Question

If A and B are two disjoint sets and N is universal set, then $A^{\circ }\cup [(A\cup B)\cap B^{\circ }]$ is

• A. $\varphi$
• B. $A$
• C. $B$
• D. $N$

Answer 1

The correct option is D $N$

In the Venn Diagram, we can see that $(A\cup B)\cap B^{\prime }$ covers the pink coloured region inside $N$ except $B$.
And $A^{\prime }$ is the region which is shown using striking lines , that is the region outside $A$
And if we perform $A^{\prime }\cup (A\cup B)\cap B^{\prime }$, it will cover the pink region as well s the striken region, which is nothing but the complete set $N$.