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

Decide,among the following sets,which sets are subsets of one another:
$A = \{ x: x \in \mathbb{R} \text{ and } x \text{ satisfies } x^2 - 8x + 12 = 0 \},$
$B = \{2, 4, 6\}, C = \{2, 4, 6, 8, \dots\}, D = \{6\}$

Which of the following is a set? Justify your answer.
The collection of all boys in your class.

Given the sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,which of the following sets can be considered as a universal set for all the three sets $A$,$B$,and $C$?
$X = \{0, 1, 2, 3, 4, 5, 6\}$

Which of the following is a set? Justify your answer.
The collection of all even integers.

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.