Question

If A and B are two given sets, then $A\cap {\left(A\cap B\right)}^c$ is equal to
(a) A
(b) B
(c) Φ
(d) $A\cap B^c$

Answer 1

(d) $A\cap B^c$
A and B are two sets.
A$\cap$B is the common region in both the sets.
${\left(\mathrm{A}\cap \mathrm{B}\right)}^c$ is all the region in the universal set except A$\cap$B.
Now,
$\mathrm{A}\cap {\left(\mathrm{A}\cap \mathrm{B}\right)}^c$ = $\mathrm{A}\cap {\mathrm{B}}^c$