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