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

(A X B) U (C X D) does not equal (A U C) X ( B U D)

Give an example of nonempty sets A,B, and C such that?
Let A = {1}, B = {1}, C = {-1}, D = {-1}


As you can see, these are nonempty steps.





By definition,





A x B = { (a, b) | a Є A and b Є B }





(A x B) = {(1,1)}


(C x D) = {(-1, -1)}





Therefore,


(A x B) U (C x D) = {(1,1)} U {(-1,-1)} = { (-1, -1) , (1, 1) }





A U C = {-1, 1}


B U D = {-1, 1}





(A U C) x (B U D) = {-1, 1} x {-1, 1}


= {(-1, -1),(-1, 1), (1, -1), (1, 1)}





As you can see,





{ (-1, -1) , (1, 1) } ≠ { (-1, -1),(-1, 1), (1, -1), (1, 1) }
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