In set-builder form,the empty set is represented by

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

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.

In a city,no two persons have an identical set of teeth,and there is no person without a tooth. Also,no person has more than $32$ teeth. If we disregard the shape and size of the teeth and consider only the presence or absence of a tooth at each of the $32$ positions,then the maximum population of the city is:

Examine whether the following statement is true or false:
$\{a\} \subset \{a, b, c\}$

List all the elements of the following set:
$D = \{ x : x \text{ is a letter in the word } \text{"LOYAL"} \}$