Image of Set Complement
Image of Set Complement
For \(f : X \to Y\)
\[ f(A)^{c} \subseteq f(A^{c}) \quad \forall A \subseteq X \iff f \ \text{is surjective}\]
with the equality condition
\[ f(A)^{c} = f(A^{c}) \quad \forall A \subseteq X \iff f \ \text{is bijective}\]