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Question: recall the following definition for two sets a and b...

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Recall the following definition: For two sets A and B, the difference set A \ B is the set consisting of those objects that are members of A but not members of B: A \ B = {x ∈ A : x 6∈ B}.

Please provide a thorough answer to the following questions.

(a) Prove or disprove: For all sets A, B, C, if A \ C = B \ C, then A = B.

(b) Prove or disprove: For all sets A, B, C, if A \ C = B \ C and C \ A = C \ B, then A = B.

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