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
$(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
If $U=\{a, b, c, d, e, f, g, h\},$ find the complements of the following sets:
$D=\{f, g, h, a\}$
Let $n(U) = 700,\,n(A) = 200,\,n(B) = 300$ and $n(A \cap B) = 100,$ then $n({A^c} \cap {B^c}) = $
Fill in the blanks to make each of the following a true statement :
$\varnothing^ {\prime}\cap A$