Show that the set of letters needed to spell "$CATARACT$" and the set of letters needed to spell "$TRACT$" are equal.

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.

Find the union of each of the following pairs of sets:
$A = \{1, 2, 3\}, B = \varnothing$

Which of the following pairs of sets are equal? Justify your answer.
$X$,the set of letters in "$ALLOY$" and $B$,the set of letters in "$LOYAL$".

If $A = \{1, 2, 3, 4, \dots, 10\}$, then the number of non-empty subsets of $A$ containing only even numbers is

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${2,3,4} \dots {1,2,3,4,5}$