(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

suppose function [tex]f : A \to B[/tex], [tex]g: A \to B[/tex], [tex]h : B \to C[/tex] satisfy [tex]g \circ f=h \circ f[/tex]. If is surjective then prove that [tex]g=h[/tex]

2. Relevant equations

n/a

3. The attempt at a solution

so for any [tex]x \in A[/tex], [tex]gf(x)=hf(x)[/tex], and for any [tex]b \in B[/tex] there exist [tex]a \in A[/tex], such that [tex]f(b)=a[/tex]

so [tex]g(a)=h(a)[/tex] so [tex]g=h[/tex] is this correct and sufficient?

i'm suppose to to show for any [tex]v \in B[/tex], [tex]g(v)=h(v)[/tex]. i don't know but something's missing.

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# Homework Help: Cancellation law with surjective functions

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