Cartesian Product

Fun Class Activity: Consider the sets $A = \{0, 1, 2\}$, $B = \{0, 2\}$, and $C = \{1, 2\}$. Answer the following questions:

1. Is the following statement true: $\{(0, 1), (2, 2)\} \subset A \times B$?
2. Is the following statement true: $\{(0, 1), (2, 2)\} \subset A \times C$?
3. What is $|A \times B|$?
4. List all the elements in $A \times B$.
5. List all the elements in $A \times C$.
6. What is $|B \times C|$?
7. List all the elements in $B \times C$.
8. Is $\emptyset \in A \times B$?
9. Is $\emptyset \subset A \times B$?