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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Label each of the following statements as either true or false.

Let f : A B where A and B are nonempty. Then f 1 ( f ( S ) ) = S for every subset S of A.

To determine

Whether the statement, ‘f1(f(S))=S for every subset S of A.’ is true or false.

Explanation

Let A={0,1}andB={0}.

A function f:AB defined by f(a)=0. Let S={0}.

Then,

f(S)={f(s)|sS}={f(0)}={0}

Also,

f1(f(S))={

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