   Chapter 6.3, Problem 54ES ### 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 , ∅ = ∅ ∩ B . 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 BU ,

B=

B= By commutative law

Take union with A on both sides, then,

A(B)

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