Pre-Image Preserves Complement Pre-Image Preserves Complement For f:X→Y and B⊆Yf−1(Bc)=f−1(B)c Proofx∈f−1(Bc)⟺f(x)∈Bc⟺f(x)∉B⟺x∉f−1(B)⟺x∈f−1(B)c