5. Let A, B, and C be subsets of some universal set U. (a) Draw two general Venn diagrams for the sets A, B, and C. On one, shade the region that represents A - (BC), and on the other, shade the region that represents (A - B) U (AC). Based on the Venn diagrams, make a conjecture about the relationship between the sets A-(BC) and (A - B) U (A–C). (b) Use the choose-an-element method to prove the conjecture from Exer- cise (5a). (c) Use the algebra of sets to prove the conjecture from Exercise (5a). 6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: ★ (a) (AB)-C = (A-C) n (B - C) (b) (AUB)(ANB) = (A — B) U (B — A)

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Q: B

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