Prove or disprove
f:A-->B
g:C-->A
h:C-->A
if f o g = f o h, then g=h,
note: o denotes the composite function.
No idea on how to do this question.
The statement in red is not true.
Consider this example: $\displaystyle A=\{a,b\},~B=\{1\},~\&~C\{x,y\}$
and $\displaystyle f=\{(a,1), (b,1)\},~g=\{(x,a),(y,b)\},~\&~h=\{(x,b),(y,a)\} $
Is it clear that $\displaystyle f \circ g = f \circ h$?
But is it true that $\displaystyle g=h$?