All but two of the following statements are correct ways to express the fact that a function f is onto. Find the two that are incorrect.

a. f is onto ⇔ every element in its co-domain is the image of some element in its domain.

b. f is onto ⇔ every element in its domain has a corresponding image in its co-domain.

c. f is onto ⇔ ∀ y ∈ Y ,   ∃ x ∈ X such that f ( x ) = y .

d. f is onto ⇔ ∀ x ∈ X ,   ∃ x ∈ Y such that f ( x ) = y .

e. f is onto ⇔ the range of f is the same as the co-domain of f.