(a) Prove or disprove: For any sets X, Y and for any map f : X Y , if there exists a map g : Y X such that g f = idX , then f is injective.

(b) Prove or disprove: For any sets X, Y and for any map f : X Y , if there exists a map g : Y X such that f g = idY , then g is surjective.

I found in internet, they said that if X and Y is empty set, then the statement is false, can I get a prove of it? Thanks.