# If A and B are two given sets,

Question:

If $A$ and $B$ are two given sets, then $A \cap(A \cap B)^{c}$ is equal to

(a) A

(b) B

(c) Φ

(d) $A \cap B^{c}$

Solution:

(d) $A \cap B^{c}$

A and B are two sets.

$A \cap B$ is the common region in both the sets.

$(\mathrm{A} \cap \mathrm{B})^{c}$ is all the region in the universal set except $\mathrm{A} \cap \mathrm{B}$.

Now,

$\mathrm{A} \cap(\mathrm{A} \cap \mathrm{B})^{c}=\mathrm{A} \cap \mathrm{B}^{c}$