For any two sets A and B,
Question:

For any two sets $A$ and $B, A \cap(A \cup B)^{\prime}$ is equal to

(a) A

(b) B

(c) $\phi$

(d) $A \cap B$                   ϕ

Solution:

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

$=A \cap\left(A^{\prime} \cap B^{\prime}\right)$   (De Morgan law)

$=\left(A \cap A^{\prime}\right) \cap B^{\prime}$

$=\phi \cap B^{\prime}$

$=\phi$

Hence, the correct answer is option (c).