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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 C implies B = C .

To determine

Whether the statement, “AB=AC” implies B=C.

Explanation

Formula Used:

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

Explanation:

Consider the statement AB=AC implies B=C.

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

Then, AB is given as,

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

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