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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 if and only if A B = A .

To determine

To prove: The statement AB if and only if AB=A.

Explanation

Formula Used:

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

Proof:

Consider the statement AB if and only if AB=A.

Suppose x(AB),

x(AB) xAandxB.

Every element of A contained in B.

Therefore, AB.

Further,

x(AB) xAandxBxA

Therefore, AAB

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