Hello,

Can anyone help me with this question please ?

Let X and Y be sets, and let f : X → Y be a function. If A c ("Contained in") X, write f[A] for the set {f(x) | x ∈ A}. Prove that f is a surjection if and only if Y − f[A] c ("Contained in") f[X − A] for all A c ("Contained in") X.

Note: c means "contained in", I am sorry because I don't know how to type this symbol in and "c" is the closest representation to it.