This page provides practice problems on Cartesian products and set sizes for Section 2.1.
1. Suppose $A = \{1, 2\}$ and $B = \{a, b\}$. Find $A \times B$.

2. Suppose $A = \{1, 2\}$ and $B = \{a, b\}$. Find $B \times A$.

3. Suppose $D = \{c, r\}$ and $C = \{c, r\}$. Find $D \times C$.

4. Suppose $Z = \{0, 1, 7, 8\}$ and $Y = \{0, 1\}$. Find $Z \times Y$.

5. Suppose $A = \{f, k\}$ and $B = \emptyset$. Find $A \times B$.

6. Suppose $V = \{f, t\}$ and $S = \{c, d, u\}$. Find $V \times S$.

7. If $A$ is a set and $|A|=5$, then what is $|\mathcal{P}(A)|$?

8. If $A$ is a set and $|A|=5$, then what is $|A \times A|$?

9. If $A = \{12, 14, 5,1\}$, what is $| (A \times A) \cup A |$?