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.
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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Transcribed Image Text:Look at the following statement proof:
Proof
Statement
1. \A, B, C ≤U, C – (AỤ B) = (Aº − C) U (Bº − C)
2.
C
(AUB) = (AUB) – C
= (AUB) NCC
3.
\A,B,C ≤U,C – (AỤ B) = (Aº − C) U (Bº − C)
4.
= (ANC) U (BNC)
= (A − C) U (B − C)
6...VA, B, C CU, C – (AUB) = (Aº − C) U (Bº − 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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