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

If $A = \{x \mid x \text{ is a prime number, } 0 \leq x \leq 9\}$,then the number of elements of the power set of $A$ is

Consider the sets $\phi, A = \{1, 3\}, B = \{1, 5, 9\}, C = \{1, 3, 5, 7, 9\}$. Insert the symbol $\subset$ or $\not\subset$ between the following pair of sets: $\phi \dots B$.

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 $\leq 5$.
Describe the event $B$ or $C$.

Show that the following four conditions are equivalent:
$(i) A \subset B, \quad (ii) A - B = \phi, \quad (iii) A \cup B = B, \quad (iv) A \cap B = A$

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.