Write the following set in roster form:
$E =$ The set of all letters in the word $TRIGONOMETRY$

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 $B = \{ x : x \in \mathbb{R} \text{ and } x^2 - 3x + 2 = 0 \}$.

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.

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 an empty set?

Assume that $P(A) = P(B)$. Show that $A = B$.