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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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Let f : A A , where A is nonempty. Prove that f a has right inverse if and only if f ( f 1 ( T ) ) = T for every subset T of A .

To determine

To prove: The function f:AA has a right inverse if and only if f(f1(T))=T for every subset T of A.

Explanation

Proof:

Consider the statements,

p: The function f:AA has a right inverse.

q: f(f1(T))=T for every subset T of A.

pq

Let aA.

Since f has a right inverse, therefore

f(f1(a))=a

Let tTA

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