If A x B C x D and A B , Prove that A C and B D.

given A × B C x D and A B

To prove: A C and B D


A × B C x D denotes A × B is subset of C × D that is every element A × B is in C × D


And A B denotes A and B does not have any common element between them.


A × B = {(a, b): a A and b B}


Since,


A × B C x D (Given)


We can say (a, b) C × D


a C and b D


A C and B D (A and B does not have common elements)


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