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.

Which of the following pairs of sets are equal? Justify your answer.
$A = \{ n : n \in \mathbb{Z} \text{ and } n^2 \le 4 \}$ and $B = \{ x : x \in \mathbb{R} \text{ and } x^2 - 3x + 2 = 0 \}$.

Write the following set in the set-builder form: $\{ 5, 25, 125, 625 \}$

Write down all the subsets of the following set: $\{a, b\}$

In the following,state whether $A=B$ or not:
$A=\{a, b, c, d\} ; B=\{d, c, b, a\}$