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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Prove or disprove that ( A B ) = ( A ) ( B ) .

To determine

Whether the statement “(AB)=(A)(B)” holds for set A and B or not.

Explanation

Formula Used:

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

Explanation:

Consider the statement (AB)=(A)(B).

Let A={3,4} and B={4,5}.

The set (AB) is given as,

(AB)={3,4}{4,5}={3,4,5}

Then, (AB) is given as,

(AB)={,{3},{4},{5},{3,4},{3,5},{4,5},{3,4

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