(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A, B, C and D are sets

if A x B is a subset of C x D then A is a subset of C and B is a subset of D.

3. The attempt at a solution

My attempt by contraposition.

Assume A is not a subset of C or B is not a subset of D. There exists an 'a' which is an element of A but is not an element of C and there exists a 'b' that is an element of B but not an element of D. 'a,b' is an element of A x B but 'a,b' is not an element of C x D. Therefore, A x B is not a subset of C X D. Thus, by contraposition, if A x B is a subset of C x D then A is a subset of C and B is a subset of D.

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# Homework Help: Proving a subset of a cartesion cross product

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