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\} $

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

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

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 an even natural number $\} $

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

$\{ x:x \in N$ and $2x + 1\, > \,10\} $

Draw appropriate Venn diagram for each of the following:

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