Give an example of nonempty sets A, B, and C such that?

(C x C)-(A x B) does not equal (C-A) x (C-B)





dealing with cartesian products and relations.





any help is appreciated

Give an example of nonempty sets A, B, and C such that?
it seems like if:





C = {1, 2}


A = B = {1}





Then


CxC = {(1, 1), (1, 2), (2, 1), (2,2)}


AxB = {(1,1)}


so


(CxC)-(AxB) = {(1, 2), (2, 1), (2,2)}





But


(C-A) = (C-B) = {2}


so


(C-A) x (C-B) = {(2,2)}





which is different from (CxC)-(AxB)

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