Question 1. Let U denote the universal set, and A, B, C be three sets of...

 

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Question 1. Let U denote the universal set, and A, B, C be three sets of U. For each of the statements below decide if it is necessarily true, or it could be false. Justify your answer with a proof or provide a counterexample. (a) C\(A\B) CAUBUC. (b) (A\B)= AC \ Bc. (c) If AC B, then B C Ac. Question 1. Let U denote the universal set, and A, B, C be three sets of U. For each of the statements below decide if it is necessarily true, or it could be false. Justify your answer with a proof or provide a counterexample. (a) C\(A\B) CAUBUC. (b) (A\B)= AC \ Bc. (c) If AC B, then B C Ac.