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3. Set Identities. Let A, B and C be sets. (a) It is tempting to say that (A – B) U (A – C) = A – (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. (A – B) U (A – C) = A – (BNC). Make use of the fact that A – B = AN B.

3. Set Identities. Let A, B and C be sets. (a) It is tempting to say that (A – B) U (A – C) = A – (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. (A – B) U (A – C) = A – (BNC). Make use of the fact that A – B = AN B.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image 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.
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