Explanation Given information: Let A,B a n d C be any set Concept used: ∪ : U n i o n of sets ∩ : I n t e r sec t i o n of sets ⊆ : subset of set Calculation: Consider the statement, If A ⊆ B then A ∩ ( B ∩ C ) c = ϕ . The objective is to verify whether the statement is true or not. Recall, the definition for complement, and, intersections Suppose A , and , B are two subsets of a universal set U . Then the complement of A is denoted by A c and is defined by A c = { x ∈ U | x ∉ A } Then, the intersection of A and B is denoted by A ∩ B and is defined by A ∩ B = { x ∈ U | x ∈ A and x ∈ B } Let A , B and C be any sets. Counter example

5th Edition

ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 6.3, Problem 11ES

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆B then A∩(B∩C)c=ϕ.

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Chapter 6.3, Problem 10ES

Chapter 6.3, Problem 12ES

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Chapter 6 Solutions

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To Prove: For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U . For all sets A , B and C , if A ⊆ B then A ∩ ( B ∩ C ) c = ϕ .

Solution Summary: The author explains how to prove each statement true and find a counterexample for each false statement.

Concept explainers

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆B then A∩(B∩C)c=ϕ.

Want to see the full answer?

Chapter 6 Solutions

To Prove: For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U . For all sets A , B and C , if A ⊆ B then A ∩ ( B ∩ C ) c = ϕ .

Solution Summary: The author explains how to prove each statement true and find a counterexample for each false statement.

Concept explainers

To Prove: For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U. For all sets A,B and C, if A⊆B then A∩(B∩C)c=ϕ.

Want to see the full answer?

Chapter 6 Solutions

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆B then A∩(B∩C)c=ϕ.