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Question -

If A x B тКЖ C x D and A тИй B тИИ тИЕ, Prove that A тКЖ C and B тКЖ D.



Answer -

Given:
A ├Ч B тКЖ C x D and A тИй B тИИ тИЕ
A ├Ч B тКЖ C x D denotes A ├Ч B is subset of C ├Ч D that is every element A ├Ч B is in C ├Ч D.
And A тИй B тИИ тИЕ denotes A and B does not have any common element between them.
A ├Ч B = {(a, b): a тИИ A and b тИИ B}
тИ┤We can say (a, b) тКЖ C ├Ч D [Since, A ├Ч B тКЖ C x D is given]
a тИИ C and b тИИ D
a тИИ A = a тИИ C
A тКЖ C
And
b тИИ B = b тИИ D
B тКЖ D
Hence proved.

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