Prove that for any f: X to Y, the relation ~f defined in x~y, if f(x)=f(y) is an equialence relation… Show more Prove that for any f: X to Y, the relation ~f defined in x~y, if f(x)=f(y) is an equialence relation. Show that for any x in X, the equivalence class of x is precisely [x]=f^-1(f(x)). • Show less