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# If P = {a, b, c} and Q = {r}, form the sets P $\times$ Q and Q $\times$ P.  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 × P.