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Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that

Q7 (b)   Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
           A \times C is a subset of B \times D

Answers (1)
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It is given that
A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}
Now,

A \times C = \left \{ (1,5),(1,6),(2,5),(2,6) \right \}
And 
B \times D = \left \{ (1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8) \right \}
We can clearly observe that all the elements of the set A \times C are the elements of the set  B \times D
Therefore, A \times C is a subset  of B \times D

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