Let A, B and C be sets. Present a direct proof for the 1. (15 point) following I

Question

Let A, B and C be sets. Present a direct proof for the 1. (15 point) following If C C A and CC B, then C C AnB. Let A, B and C be sets. Present a direct proof for the 2. (15 point) following: A _ (BUC) (A-B) n (A-C). 3. Let A, B and C be sets (a) (5 point) Present a direct proof for the following (A-B)-CSA-(B-C). Give a counterexample and provide a precise (b) (1o point) explanation to the following false statement: A-(B-C) (A-B)-C. Let A and B be sets. (a) (5 point) Present a direct proof for the following (b) (10 point) Give a counterexample and provide a precise explanation to the following false statement: 2AUB 24u28 5. (20 point)) Present a direct proof for the following: Let A, B, C and D be sets. Then (A n B) (C n D) = (A x C) n (B × D).

Explanation / Answer

1. Let

x A B this means x A and x B  

and C A (Given) and C B ( Given)  

thus x C

Now from above conclusion

x C and x AB

hence C A B  

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