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(a) Give an argument (not using Venn diagrams) to prove that for any three sets A,...

(a) Give an argument (not using Venn diagrams) to prove that for any three sets A, B, and C, we have (A∪B)−C ⊆(A−(B∪C))∪(B−(A∩C)).

(b) Does the equality (A∪B)−C=(A−(B∪C))∪(B−(A∩C)) hold for all sets A, B, and C? If so, prove it; if not, give three sets for which the equality fails.

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