   Chapter 6.3, Problem 30ES ### 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
1 views

# 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,B, and C, ( A ∩ B ) ∪ C = ( A ∩ C ) ∩ ( B ∪ C ) .

To determine

To prove:

For all sets A,B,andC,

(AB)C=(AC)(BC)

Explanation

Given information

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

Concept used:

(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 the following result,

“If A,B,C are any three sets, then (AB)C=(AC)(BC)

The objective is to prove the above result by using the identities in sets

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