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6. The following statements about sets are false. For each statement, give an example, i.e., a choice of sets, for which the statement is false. Such examples are called counterexamples. They are examples that are counter to i.e., contrary to, the assertion. (a) AUBSAN B for all A, B. (b) ANØ = A for all A. (c) AN (BUC) = (ANB) UC for all A, B, C.

6. The following statements about sets are false. For each statement, give an example, i.e., a choice of sets, for which the statement is false. Such examples are called counterexamples. They are examples that are counter to i.e., contrary to, the assertion. (a) AUBSAN B for all A, B. (b) ANØ = A for all A. (c) AN (BUC) = (ANB) UC for all A, B, C.

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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6. The following statements about sets are false. For each statement, give an example, i.e., a choice of sets, for which the statement is false. Such examples are called counterexamples. They are examples that are counter to, i.e., contrary to, the assertion. (a) AUBCAn B for all A, B. (b) ANØ: = A for all A. (c) AN (BUC) = (A ^ B) UC for all A, B, C.
Transcribed Image Text:6. The following statements about sets are false. For each statement, give an example, i.e., a choice of sets, for which the statement is false. Such examples are called counterexamples. They are examples that are counter to, i.e., contrary to, the assertion. (a) AUBCAn B for all A, B. (b) ANØ: = A for all A. (c) AN (BUC) = (A ^ B) UC for all A, B, C.
Expert Solution
Step 1

What is Counter Example:

A counterexample is an illustration that meets the criteria for a mathematical assertion but does not lead to the conclusion of the statement. Counterexamples are used to show a statement to be false. Identify the premise and conclusion of the given statement. The counterexample must be true in order for the hypothesis to be correct but the conclusion to be incorrect.

Given:

Given statements are:

For all A,B, A∪B⊆A∩B.

For all A, A∩∅=A. 

For all A,B,C, A∩B∪C=A∩B∪C.

To Determine:

For each statement, we give counter example to show the invalidity of the statements.

steps

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