Cartesian Product/Examples/Product of Arbitrary Sets 2

Examples of Cartesian Products

Let $V = \set {v_1, v_2}$.

Let $W = \set {w_1, w_2, w_3}$.

Then:

\(\ds V \times W\)

\(=\)

\(\ds \set {\tuple {v_1, w_1}, \tuple {v_1, w_2}, \tuple {v_1, w_3}, \tuple {v_2, w_1}, \tuple {v_2, w_2}, \tuple {v_2, w_3} }\)

\(\ds V \times V\)

\(=\)

\(\ds \set {\tuple {v_1, v_1}, \tuple {v_1, v_2}, \tuple {v_2, v_1}, \tuple {v_2, v_2} }\)

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.2$: Cartesian Products and Relations