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

Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{ x: x \ge 7 \}$

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{2, 4, 6, 8\}$,and $B = \{2, 3, 5, 7\}$,verify that $(A \cap B)^{\prime} = A^{\prime} \cup B^{\prime}$.

Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{ x : x \text{ is an odd natural number} \}$

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 $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$,$A = \{1, 2, 5\}$,and $B = \{6, 7\}$. Find $A \cap B'$.