Explanation Given information: Let A and B 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 following statement, P ( A ) ∪ P ( B ) ⊆ P ( A ∪ B ) The objective is to verify whether the statement is true or not. Recall, the definition for a power set. A Power Set is a set of all the subsets of a set. Let A and B are two sets, then the Power Sets of A and B are defined by, P ( A ) = { X | X is a subset of A } and P ( B ) = { X | X is a subset of B } The sets in P ( A ) ∪ P ( B ) contains only sets that are subsets of either A and B , and P ( A ∪ B ) contains the elements of both the sets A and B . Let A and B are two subsets of a universal set U then

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 19ES

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 and B, P(A)∪P(B)⊆P(A∪B).

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Chapter 6 Solutions

Discrete Mathematics With Applications

Ch. 6.1 - The notation is read”______” and means that___Ch. 6.1 - To use an element argument for proving that a set...Ch. 6.1 - Prob. 3TY Ch. 6.1 - An element x is in AB if , and only if,_______Ch. 6.1 - An element x in AB if, and only if,______Ch. 6.1 - An element x is in B-A if, and only if,______Ch. 6.1 - An elements x is in Acif, and only if.______Ch. 6.1 - The empty set is a set with ______Ch. 6.1 - The power set of a set A is _____Ch. 6.1 - Prob. 10TY

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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 and B , P ( A ) ∪ P ( B ) ⊆ P ( A ∪ B ) .

Solution Summary: The author explains the definition of a power set, wherein the objective is to verify whether the statement is true or not.

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 and B, P(A)∪P(B)⊆P(A∪B).

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 and B , P ( A ) ∪ P ( B ) ⊆ P ( A ∪ B ) .

Solution Summary: The author explains the definition of a power set, wherein the objective is to verify whether the statement is true or not.

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 and B, P(A)∪P(B)⊆P(A∪B).

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 and B, P(A)∪P(B)⊆P(A∪B).