   Chapter 6.3, Problem 42ES ### 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 41-43 simplify the given expression. Cite a property from Theorem 6.2.2 for every step. ( A − ( A ∩ B ) ) ∩ ( B − ( A ∩ B ) )

To determine

To prove:

(A(AB))(B(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)Cc               By 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 the sets A and B

(A( AB))(B( AB))={A( AB)c}{B(

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