WA 3 - N icola Hodges David Walnut MATH 290-002 September...

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Nicola Hodges David Walnut MATH 290-002 September 28, 2010 Writing Assignment 3 1. Prove that any sets A and B, (A – B) U (B – A) = (A U B) – (A B) First we will show (A – B) U (B – A) (A U B) – (A B). Assume x [(A – B) U (B – A) ]. So x A and X B or x B and X A. First assume x A and hence X B. So x (A U B) and x (A B) So, x (A U B) – (A B). Second, assume x B and hence X A. So x (A U B) and x (A B) So, x (A U B) – (A B). Therefore, (A – B) U (B – A) (A U B) – (A B). Next we will show that (A U B) – (A B) (A – B) U (B – A). Assume x (A U B) and x (A B) So x A or x B, but x A and B. First assume x A, and Since x (A B), x B. Hence, x (A – B) and x (B – A) So, x (A – B) U (B – A) Second, assume x B Since, x (A B), x A. Hence, x
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WA 3 - N icola Hodges David Walnut MATH 290-002 September...

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