3. Set Identities. Let A, B and C be sets. (a) It is tempting to say that (А — В) U (A— C) %3 А — (BUC). Provide a counterexample to show that the statement is false. Note: the sizes of A, B and C...

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Extracted text: 3. Set Identities. Let A, B and C be sets. (a) It is tempting to say that (А — В) U (A— C) %3 А — (BUC). Provide a counterexample to show that the statement is false. Note: the sizes of A, B and C need not be big – e.g., at most 3. (b) Now prove using set identities that the following is true. Make sure that you write the set identity that you used at each step. (А — В) U (A— C) %3 А — (BnС). Make use of the fact that A – B = AnB.