2.2 Examples of Cartesian Products

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 2.1 Cross Product of Sets

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Senator Voting Map

Let

\begin{aligned} A & = {- 1, 0, 1} \\ B & = {Nay, Yay, Abstain} \end{aligned}

Then, find $A \times B$ .

Solution. Let's write out $A \times B$ using 1.2 Element Enumeration.

A \times B = \begin{matrix} { & (- 1, Nay), & (- 1, Yay), & (- 1, Abstain), \\ (0, Nay), & (0, Yay), & (0, Abstain), \\ (1, Nay), & (1, Yay), & (1, Abstain) & } \end{matrix}

Alphabet

Let

\begin{aligned} U & = {A, B, C, \dots, Z} \\ [26] & = {1, 2, 3, \dots, 26} \end{aligned}

Then, find $U \times [26]$ .

Solution.

U \times [26] = \begin{matrix} { & (A, 1), & (A, 2), & (A, 3), & \dots, & (A, 26) \\ (B, 1), & (B, 2), & (B, 3), & \dots, & (B, 26) \\ ⋮ \\ (Z, 1), & (Z, 2), & (Z, 3), & \dots, & (Z, 26) & } \end{matrix}