Let f: X->Y and g:Y->X be maps between sets. Suppose that g ∘ f is equal to the identity map id_X: X->X. Does it follow that f ∘ g is equal to the identity map id_Y:Y->Y? Give a proof or a counterexample.

Let f: X->Y and g:Y->X be maps between sets. Suppose that g ∘ f is equal to the identity map id_X: X->X. Does it follow that f ∘ g is equal to the identity map id_Y:Y->Y? Give a proof or a counterexample.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 29E: 29. Suppose , , represents a partition of the nonempty set A. Define R on A by if and only if there...

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