   Chapter 1.5, Problem 1TFE

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Textbook Problem
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# True or FalseLabel each of the following statements as either true or false.Every permutation has an inverse.

To determine

Whether the statement, ‘Every permutation has an inverse’ is true or false.

Explanation

Consider the provided statement ‘Every permutation has an inverse.’

Suppose that f is a permutation on A. Then f has left inverse as it is one-one

This means there exist left inverse g such that gf=IA, where IA is the identity.

Also f has right inverse as it is onto.

This means there exist right inverse h such that fh=IA

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