   Chapter 6.3, Problem 37ES ### 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.For all sets A and B, ( B x ∪ ( B e − A ) ) x = B .

To determine

To prove:

(Bc( B c A))c=B

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

Calculation:

Let A and B be any sets, then

(Bc( B c A))c=B

The objective is to provide an algebraic proof for ¡ne above statement by mentioning appropriate properties for each step of the proof

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