   Chapter 6.3, Problem 29ES ### 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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# Some steps are missing from the following proof that for all sets A and B, ( A ∪ B e ) − B = ( A − B ) ∪ B e . Indicate what they are, and then write the proof correctly. Proof: Let any sets A and B be given. Then

To determine

Some steps are missing from the following proof that for all sets

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

Indicate what they are, and then write the proof correctly.

Proof:

Let A,B,and C  be any sets. Then

(AB)C=(AB)Ccby the set difference law=(ACc)(BCc)by the distributive law=(AC)(BC)by the set difference law

Explanation

Given information Let A,BandC be any three sets.

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

Therefore,

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

Concept used:

(AB)C=(AB)Ccby the set difference law=(ACc)(BCc)by the distributive law=(AC)(BC)by the set difference law

Calculation:

Let A,BandC be any three sets

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