Write the following set in roster form:
$B = \{x : x \text{ is a natural number less than } 6\}$

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.

If $A, B,$ and $C$ are three sets,then $A \cap (B \cup C) =$

Write the following interval in set-builder form: $(-3, 0)$

Prove that for any sets $A$ and $B$,$A \cap (A \cup B) = A$.

Write the following set in the set-builder form: $\{ 1, 4, 9, \ldots, 100 \}$