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

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

Let $U$ be the universal set and $A \cup B \cup C = U$. Then $\{ (A - B) \cup (B - C) \cup (C - A)\} '$ is equal to

Let $U=\{1,2,3,4,5,6\}, A=\{2,3\}$ and $B=\{3,4,5\}$

Find $A^{\prime}, B^{\prime}, A^{\prime} \cap B^{\prime}, A \cup B$ and hence show that $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$

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

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

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\} $

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

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