Fill in the blanks to make each of the following a true statement:
$A \cup A^{\prime} = \ldots$

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 $(A')'$.

If $A$ is any set,then:

If $U = \{a, b, c, d, e, f, g, h\}$,find the complement of the set $A = \{a, b, c\}$.

Let $U = \{1, 2, 3, 4, 5, 6\}$,$A = \{2, 3\}$,and $B = \{3, 4, 5\}$. Find $A'$,$B'$,$A' \cap B'$,$A \cup B$,and hence show that $(A \cup B)' = A' \cap B'$.

Draw an appropriate Venn diagram for the following: $(A \cap B)^{\prime}$