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Show that if f : A ->B and g : B ->Care ...

Show that if `f : A ->B` and `g : B ->C`are onto, then `gof : A ->C` is also onto.

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To show that if \( f: A \to B \) and \( g: B \to C \) are onto functions, then the composition \( g \circ f: A \to C \) is also onto, we will follow these steps: ### Step 1: Understand the Definition of Onto Functions An onto function (or surjection) is defined such that for every element \( y \) in the codomain \( Y \), there exists at least one element \( x \) in the domain \( X \) such that \( h(x) = y \). ### Step 2: Given Functions We are given two functions: - \( f: A \to B \) is onto, meaning for every \( b \in B \), there exists \( a \in A \) such that \( f(a) = b \). ...
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