I need your help with the following task: I have to prove:
If $ \sim $ is an equivalence relation on a set $ A $ and if $ C=\{[a ]_\sim \mid a \in A\} $ is the set of equivalence classes of $ \sim $, then there is a function $ p: A \longrightarrow C $ such that for all $ a_{1}, a_{2} \in A : a_{1} \sim a_{2} \Longleftrightarrow p\left(a_{1}\right)=p\left(a_{2}\right)$