If $P=\{a, b, c\}$ and $Q=\{r\},$ form the sets $P \times Q$ and $P \times Q$ Are these two products equal?
If $P=\{a, b, c\}$ and $Q=\{r\},$ form the sets $P \times Q$ and $P \times Q$ Are these two products equal?
By the definition of the cartesian product.
$P \times Q =\{(a, r),(b, r),(c, r)\}$ and $Q \times P =\{(r, a),(r, b),(r, c)\}$
Since, by the definition of equality of ordered pairs, the pair $(a, r)$ is not equal to the pair $(r, a),$ we conclude that $P \times Q \neq Q \times P$
However, the number of elements in each set will be the same.
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