Look at the following statement proof: Proof Statement 1. VA, B, CCU,C – (AUB) = (Aº – C) U (Bº − C) 2. C (AUB) = (A U B) – C = (AUB) nCc 3. VA, B,CCU,C− (AUB) = (Aº – C) U (B − C) 4. = (AnC)u(BNC) = (A − C) U (B − C) 6...VA, B,CCU, C – (AUB) = (A¢ − C) U (B − C) 5. Justification To be proved. Commutativity. Set difference law. Distribution law. Set difference law. Transitivity of equality. a. Find a counterexample with three non-empty sets that shows that the statement to be proved is false. Justify your counterexample. b. Find at least one statement in the proof that is not correct and create a counterexample with non-empty sets to prove your assertion. Justify your counterexample.

Look at the following statement proof: Proof Statement 1. VA, B, CCU,C – (AUB) = (Aº – C) U (Bº − C) 2. C (AUB) = (A U B) – C = (AUB) nCc 3. VA, B,CCU,C− (AUB) = (Aº – C) U (B − C) 4. = (AnC)u(BNC) = (A − C) U (B − C) 6...VA, B,CCU, C – (AUB) = (A¢ − C) U (B − C) 5. Justification To be proved. Commutativity. Set difference law. Distribution law. Set difference law. Transitivity of equality. a. Find a counterexample with three non-empty sets that shows that the statement to be proved is false. Justify your counterexample. b. Find at least one statement in the proof that is not correct and create a counterexample with non-empty sets to prove your assertion. Justify your counterexample.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.5: Applications Of Inner Product Spaces

Problem 66E

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