Question

If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

Answer 1

Solution:  By the definition of the cartesian product,
P × Q = {(a, r ), (b, r), (c, r)} and Q × 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 × Q ¹ Q × P.
However, the number of elements in each set will be the same.