List all the elements of the following set:
$D = \{ x : x \text{ is a letter in the word } \text{"LOYAL"} \}$

Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C = \varnothing$.

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.

How many elements does $P(A)$ have,if $A = \varnothing$?

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

List all the elements of the following set:
$C = \{ x : x \text{ is an integer; } x^2 \le 4 \}$