   Chapter 6.3, Problem 35ES ### 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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# In 30—40, construct an algebraic proof for the given statement. Cite a property from Theorem 6.2.2 for every step. 35. For all sets A and B, A − ( A − B ) = A ∩ B .

To determine

To prove:

For all sets Aand B, A(AB)=AB.

Explanation

Given information

(AB)C=(AC)(BC).

Concept used:

(AB)C=(AC)(BC).

Cite a property from Theorem 6.2.2 for every step of the proof.

Solution: Let A,B,and C be any sets. Then

(AB)C=(AB)Ccby the set difference law=Cc(AB)by the commutative law for =(CcA)(CcB)by the distributive law=(ACc)(BCc)by the commutative law for =(AC)(BC)by the set difference law.

Calculation:

Consider that Aand B be any two sets.

The objective is to construct an algebraic proof of the following statement.

A(AB)=AB

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