Question

If A = {1, 3, 5, ..... ,17}, B ={2, 4, 6, ..... ,18} and N, the set of natural numbers is the universal set, then $(A^{\prime }\cup [(A\cup B)\cap B^{\prime }\left]\right)$ is

• A. $\varphi$
• B. N
• C. A
• D. B

Answer 1

The correct option is B

N

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