solve question e) Let A and B be subsets of some universal set U. Prove that A a

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solve question e)

Let A and B be subsets of some universal set U. Prove that A and B - A are disjoint sets. Prove that A B = A (B - A). Let A and B be subsets of some universal set U. Prove that A - B and A B are disjoint sets. Prove that A = (A - B) (A B). Let A and B be subset of some universal set U. Prove or disprove each of the following: A - (A Bc) = A B (Ac B)c A = A - B (A B) - A = B - A (A B) - B = A - (A B) (A B) - (A B) = (A - B) (B - A) Evaluation of proofs See the instructions for Exercise (15) on pace from Section 3.1. If A, B, and C are subsets of some universal set U, then A - (B - C) = A - (B C).

Explanation / Answer

Left hand side: (A U B) - (A intersection B) = (A U B) intersection (A intersection B)' = (A U B) intersection (B' U A') = (A intersection B') U (A intersection A') U B intersection B') U (B intersection A') = (A - B) U (null set) U (null set) U (B - A) = (A - B) U (B - A) = Right hand side

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