State whether the following set is finite or infinite:
The set of numbers which are multiples of $5$.

Let $P$ and $T$ be the subsets of the $xy$-plane defined by $P = \{(x, y) : x > 0, y > 0 \text{ and } x^2 + y^2 = 1\}$ and $T = \{(x, y) : x > 0, y > 0 \text{ and } x^8 + y^8 < 1\}$. Then, $P \cap T$ is

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
$\{\varnothing\} \subset A$

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.

Which of the following sets is a subset of all other sets?

Prove that for any sets $A$ and $B$,$A \cap (A \cup B) = A$.