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prettymidget

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## Homework Statement

Prove or disprove

a) Let f:X---->Y. If f possesses more than 1 left inverse yet has no right inverse, then f has strictly more than 1 left inverse.

b) If f and g are maps from a set X to X and fog is one to one, then f an g are both injective one to one.

## Homework Equations

## The Attempt at a Solution

a) I came across a counterexample.

f: A -> B where A = {1}, B = {1,2} and f(1)=1b) I know it can be false when f maps X to Y since the only inner function need be one to one , but I am not positive about when it maps to itself. I think the statement becomes true. Amirite?

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