   Chapter 6.3, Problem 27ES ### 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 27 and 28 supply a reason fro each step in the derivation.Forall sets A, B, and C, ( A ∪ B ) ∩ C = ( A ∩ C ) ∪ ( B ∩ C ) Proof: Suppose A, B, and C, are any sets. Then ( A ∪ B ) ∩ C = C ∩ ( A ∪ B )                                                                                 by(a) = C ∩ ( A ∪ B )                                                                                 by(b) = ( A ∩ C )   ∪ ( B ∩ C )                                                         by(c)

To determine

For all sets A,B,and C,

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

Proof:

Suppose A,B,and C are any sets. Then

(AB)C=C(AB)by (a)=(CA)(CB)by (b)=(AC)(BC)by (c)

Explanation

Given information

(AB)C=C(AB)by (a)(AB)C=(CA)(CB)by (b)(AB)C=(AC)(BC)by (c)

Concept used:

(AB)C=C(AB)by the commutative law for(AB)C=(CA)(CB)by the distributive law(AB)C=(AC)(BC)by the commutative law for

Calculati

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