Draw appropriate Venn diagram for each of the following:

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

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 $U$)

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

${{\mathop{\rm U}\nolimits} ^\prime } \cap A =  \ldots $

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

$\{ x:x$ is a natural number divisible by $ 3 $ and $5\} $

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

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

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

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