Which of the following is an example of the null set?
$\{ x : x \in \mathbb{N}, x < 5 \text{ and } x > 7 \}$

If $A$ and $B$ are two sets,then $A \cup B = A \cap B$ if and only if

Examine whether the following statement is true or false:
$\{x : x \text{ is an even natural number less than } 6\} \subset \{x : x \text{ is a natural number which divides } 36\}$

Find the union of each of the following pairs of sets:
$A = \{1, 2, 3\}, B = \varnothing$

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 $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B^{\prime}$ are mutually exclusive.

State whether the following set is finite or infinite:
The set of circles passing through the origin $(0,0)$.