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:
$A = \{ x : x \text{ is a perfect square} \}$

If $A$ and $B$ are two sets,then $A \cap (A \cup B)'$ is equal to

If $A$ and $B$ are any two sets,then $(A \cap B)'$ is equal to

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 $B^{\prime}$.

Which of the following statements is false (where $A$ and $B$ are two non-empty sets)?