Homework Proofs

# Homework Proofs - Assume x ∈(A – B – C So x ∈ A but...

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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) Assume x [(A – B) U (B – A) ]. So [x A X B ] V [x B X A ]. Hence, x (A B). Which is equivalent to, x (A B). Therefore x ( A V B) and x (A Λ B). Which is equivalent to, (A U B) – (A B). (A – B) U (B – A) = (A U B) – (A B) 2. Prove that for any sets A, B, and C, (A – B) – C = (A – C) – (B – C)

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Unformatted text preview: Assume, x ∈ [(A – B) – C]. So, x ∈ A, but x ∉ B and x ∉ C. B – C is a subset of B. X ∉ B, therefore, x ∉ (B – C). Hence x ∉ A – (B – C) Therefore, (A – B) – C = (A – C) – (B – C). 3. a. Prove that for any sets A and B, P(A) U P (B) ⊆ P(A U B) b. Find an example of two sets A and B, such that, P(A) U P(B) = P (A U B) c. Find an example of two sets A and B, such that, P(A) U P(B) P (A U B) ≠...
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## This note was uploaded on 03/05/2011 for the course MATH 290 taught by Professor Alligood,k during the Fall '08 term at George Mason.

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Homework Proofs - Assume x ∈(A – B – C So x ∈ A but...

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