If A={1,2}, B= {1,2,3,4}, C={5,6}and D= {5,6,7,8},then check A×C

1.	If A={1,2}, B= {1,2,3,4}, C={5,6}and D= {5,6,7,8},then check A×C is a subset of B×D or not.
Answer» A = {1,2}, B = {1,2,3,4} C = {5,6} D = {5,6,7,8} A x C = {(1,5),(1,6),(2,5),(2,6)} B x D = {(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)} Clearly, A x C \(\subseteq\) B x D Alternate : A \(\subseteq\) B & C \(\subseteq\) D ∴ A x C \(\subseteq\) B x D.

If A={1,2}, B= {1,2,3,4}, C={5,6}and D= {5,6,7,8},then check A×C is a subset of B×D or not.

Answer»

A = {1,2},

B = {1,2,3,4}

C = {5,6}

D = {5,6,7,8}

A x C = {(1,5),(1,6),(2,5),(2,6)}

B x D = {(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)}

Clearly,

A x C \(\subseteq\) B x D

Alternate :

A \(\subseteq\) B & C \(\subseteq\) D

∴ A x C \(\subseteq\) B x D.

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If A={1,2}, B= {1,2,3,4}, C={5,6}and D= {5,6,7,8},then check A×C is a subset of B×D or not.

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