Consider the proposed proof of the statement Proof Statement 1. VA, B, CCU,C- (AUB) = (Aº - C) U (B² – C) 2. C (AUB) = (AUB) – C = (AUB) NCC = (ANC) U (BNC) = (A-C) U (B-C) 6...VA, B, CCU, C- (AUB) = (A - C) U (B-C) 3. 4. VA, B, CCU,C- (AUB) = (A - C) U (BCC) 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.
Consider the proposed proof of the statement Proof Statement 1. VA, B, CCU,C- (AUB) = (Aº - C) U (B² – C) 2. C (AUB) = (AUB) – C = (AUB) NCC = (ANC) U (BNC) = (A-C) U (B-C) 6...VA, B, CCU, C- (AUB) = (A - C) U (B-C) 3. 4. VA, B, CCU,C- (AUB) = (A - C) U (BCC) 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.
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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URGENT
Transcribed Image Text:Consider the proposed proof of the statement
Proof
Statement
1. VA, B, C CU,C – (AUB) = (Aª − C) U (Bª − C)
2.
C – (AUB) = (A U B) – C
= (AUB) NCC
3.
VA, B, CCU,C – (AUB) = (Aª − C) U (B¤ − C')
4.
= (ANC)U(BNC“)
= (A − C) U (B − C)
6. .. \A, B,CCU,C – (AUB) = (Aº − C) U (Bª − 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.
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