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Question

Given : A = {2, 3}, B = {4, 5}, C = {5, 6}, then prove the following :
(A×B)(B×C) = {(2, 4), (2, 5), (3, 4), (3, 5)} {(4, 5), (4, 6), (5, 5), (5, 6)} = All the ordered pairs as they are disjoint.

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Solution

A=(2,3}; B=(4,5}; C=(5,6}
(A×B)=((2,4),(2,5),(3,4),(3,5)}
(B×C)=((4,5),(4,6),(5,5),(5,6)}
(A×B)(B×C)=((2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,5),(5,6)}
Hence all the ordered pairs are disjoint.

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