Fill in the blank to make the following a true statement:
$U^{\prime} \cap A = \ldots$

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

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

If $A$ and $B$ are two given sets,then $A \cap (A \cap B)^c$ is equal to

Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{ x : x \text{ is a perfect square} \}$

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $\text{not } B$.