If $P = \{a, b, c\}$ and $Q = \{r\}$,find the sets $P \times Q$ and $Q \times P$. Are these two products equal?

(B) By the definition of the Cartesian product:
$P \times Q = \{(a, r), (b, r), (c, r)\}$
$Q \times P = \{(r, a), (r, b), (r, c)\}$
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 is the same.