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# WA 4 - Nicola Hodges David Walnut MATH 290-002 October 5...

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Nicola Hodges David Walnut MATH 290-002 October 5, 2010 Writing Assignment 4 1. Prove that any sets A and B, (A x B) (B x A) = (A B) x (A B) Show, (A x B) (B x A) (A B) x (A B). Let (x,y) [ (A x B) (B x A) ]. So (x,y) (A x B) and (x,y) (B x A). Since (x,y) (A x B) then, x A and y B. Since (x,y) (B x A) then, x B and y A. Since x A and x B, (A B), Since y B and y A, (A B). Therefore, (x,y) (A B) x (A B). So, (A x B) (B x A) (A B) x (A B). Show (A B) x (A B) (A x B) (B x A). Let (x,y) [ (A B) x (A B) ]. So, x (A B) and y (A B). Since x (A B) then, x A and x B. Since y (A B) then, y A and y B. Since, x A and y B, then (x,y) (A x B). Since, x B and y A, then (x,y) (B x A). Therefore, (x,y) (A x B) (B x A). So, (A B) x (A B) (A x B) (B x A). Therefore, (A x B) (B x A) = (A B) x (A B).

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Allow: A α to be represented by U a ∈∆ A a.
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WA 4 - Nicola Hodges David Walnut MATH 290-002 October 5...

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