Question

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B ={2, 4, ......, 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

Using distributive property of sets (intersection over union), we have
$A^{\prime }\cup \left[\right(A\cup B)\cap B^{\prime }]=A^{\prime }\cup \left[\right(A\cap B^{\prime })\cup (B\cap B^{\prime }\left)\right]=A^{\prime }\cup \left[\right(A\cap B^{\prime })\cup \varphi ]=A^{\prime }\cup (A\cap B^{\prime })=(A^{\prime }\cup A)\cap (A^{\prime }\cup B^{\prime })=N\cap (A\cap B{)}^{\prime }=(A\cap B{)}^{\prime }={\varphi }^{\prime }=N.$