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 $\} $
If $A$ and $B$ are two sets, then $A \cap (A \cup B)'$ is equal to
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 $U=\{1,2,3,4,5,6,7,8,9\}, A=\{1,2,3,4\}, B=\{2,4,6,8\}$ and $C=\{3,4,5,6\} .$ Find
$(A \cup C)^{\prime}$