   Chapter 6.3, Problem 32ES ### 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 and B, ( A − B ) ∪ ( A ∩ B ) = A .

To determine

To prove:

For all sets Aand B,

(AB)(AB)=A.

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 statement as,

“For all sets Aand B,(AB)(AB)=A

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