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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 set B.

Explanation

Formula Used:

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

Explanation:

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

Let A={1,2,3} and B={3,4,5}.

The set (AB) is given as,

(AB)={1,2,3}{3,4,5}={1,2}

Then, (AB) is given as,

(AB)={,{1},{2},{1,2}}

And (A)(B) is given as,

(A)(B)={,{1},

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