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

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

$\{ x:x$ is a perfect cube $\} $

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

$\{ x:x$ is a perfect square $\} $

Let $U=\{1,2,3,4,5,6,7,8,9\}, A=\{1,2,3,4\}, B=\{2,4,6,8\}$ and $C=\{3,4,5,6\} .$ Find

$(A \cup C)^{\prime}$

If $U =\{1,2,3,4,5,6,7,8,9\}, A =\{2,4,6,8\}$ and $B =\{2,3,5,7\} .$ Verify that

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