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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?
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Jun 24, 2014
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thanvigandhi_1
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Jun 25, 2014
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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.
However, the number of elements in each set will be the same.
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Jun 24, 2014
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thanvigandhi_1
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