   Chapter 1.5, Problem 5E

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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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