   Chapter 6.3, Problem 53ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Derive the set identity A ∪ ( A ∩ B ) = A from the properties listed in Theorem 6.2.2.(1)-(9) Start by showing that for every subset B of a universal set U , U ∪ B = U Then intersect both sides with A and deduce the identity.

To determine

To derive:

A(AB)=A

Explanation

Given information:

A and B be any sets.

Concept used:

AΔB=(AB)(BA)

Calculation:

The objective is to derive the following identity by using the known properties.

A(AB)=A

To derive this identity, use the universal bound law.

By the universal bound law, it is clear that for all subsets B of a universal set U ,

UB=U

Intersect both sides with A then,

A(UB<

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