Explanation Given information: Let A,B and 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 ⊆ C and B ⊆ C then A ∪ B ⊆ C . The objective is to verify whether the statement is true or not. Recall, the definition for Unions, and, Intersections Suppose A and B are two subsets of a universal set U . For a set A to be a subset of a set B is denoted by A ⊆ B and is defined by A ⊆ B : { ∀ x , if x ∈ A then x ∈ B }

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 9ES

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⊆C and B⊆C then A∪B⊆C

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Chapter 6.3, Problem 8ES

Chapter 6.3, Problem 10ES

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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 ⊆ C and B ⊆ C then A ∪ B ⊆ C

Solution Summary: The author explains how to prove each statement that is 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⊆C and B⊆C then A∪B⊆C

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 ⊆ C and B ⊆ C then A ∪ B ⊆ C

Solution Summary: The author explains how to prove each statement that is 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⊆C and B⊆C then A∪B⊆C

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⊆C and B⊆C then A∪B⊆C