Subset Product/Singleton/Examples/Subsets of Reals under Multiplication

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Example of Subset Product

Let $\struct {\R, \times}$ be the multiplicative group of (non-zero) real numbers.

Let $S = \set 3$.

Let $T = \set {-1, 2}$.

Then the subset product $S T$ is:

$ST = \set {-3, 6}$


Proof

Taking each ordered pair $\tuple {s, t}$ from $S \times T$:

\(\ds 3 \times -1\) \(=\) \(\ds -3\)
\(\ds 3 \times 2\) \(=\) \(\ds 6\)

$\blacksquare$


Sources