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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 B ) ( A B ) = A

To determine

To prove: The statement (AB)(AB)=A.

Explanation

Formula Used:

A={xU|xA} where A is the subset of universal set U.

If A and B are two sets then AB is defined as {x|xAandxB}.

If A and B are two sets then AB is defined as {x|xAorxB}.

If A and B are two sets then AB is defined as {x|xAandxB}.

Proof:

Let x(AB)(AB).

Now,

x(AB)(AB)x(AB) or x(AB)

If,

xABxAandxBxA

If,

xABxAandx<

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