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