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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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In Exercises 14-35, prove each statement.

A ( A ' B ) = A B

To determine

To prove: A(A'B)=AB

Explanation

Formula used:

1) Complement:

A' is defined as A'=UA={xU|xA} the set A' ( read as complement of A ’) where U is universal set.

AA'=U and AA'=ϕ

2) Distributive law:

A(BC)=(AB)(AC)

A(BC)=(AB)(AC)

Proof:

Let A(A'

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