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

If $n(A) = 3$ and $n(B) = 6$ and $A \subseteq B$,then the number of elements in $A \cap B$ is:

The solution set of $x \equiv 3 \pmod{7}$,where $p \in \mathbb{Z}$,is given by:

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.

Write the following interval in set-builder form: $[6, 12]$

Let the set $C = \{(x, y) \mid x^2 - 2^y = 2023, x, y \in \mathbb{N}\}$. Then $\sum_{(x, y) \in C} (x + y)$ is equal to