Fill in the blanks to make each of the following a true statement :

$A \cap A^{\prime}=\ldots$

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

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

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

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

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

$\left(A^{\prime}\right)^{\prime}$

If $n(U)$ = $600$ , $n(A)$ = $100$ , $n(B)$ = $200$ and $n(A \cap  B )$ = $50$, then $n(\bar A  \cap \bar B )$ is 

($U$ is universal set and $A$ and $B$ are subsets of $U$)

Draw appropriate Venn diagram for each of the following:

$A^{\prime} \cap B^{\prime}$