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[University Math] Intro to proofs course, set theory and the cartesian product
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ghostof_IamBeepBeep2 is
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University Math
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The question is
Is it true that (AxA)(BxB) = (A\B)x(A\B) for any two sets A,B? If it is true, prove it. Otherwise, find a counterexample.
I've done some rough work with two examples and based off these two it seems like this identity is true, and so now I'll have to try and prove it.
https://i.imgur.com/5bzSDFC.jpg
I was just posting to make sure my understanding of AxA is correct since the cartesian production of a single set is not something that is mentioned in the course notes.
Also does anyone have any idea on how I can go about starting this proof, if there is one?
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