All but two of the following statements are correct ways to express the fact that a

Chapter 7, Problem 5

(choose chapter or problem)

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 \(\Leftrightarrow\) every element in its co-domain is the image of some element in its domain.

b. f is onto \(\Leftrightarrow\) every element in its domain has a corresponding image in its co-domain.

c. f is onto \(\Leftrightarrow \forall y \in Y, \exists x \in X\) such that f (x) = y.

d. f is onto \(\Leftrightarrow \forall x \in X, \exists y \in Y\) such that f (x) = y.

e. f is onto \(\Leftrightarrow\) the range of f is the same as the co-domain of f .

Text Transcription:

Leftrightarrow

Leftrightarrow

Leftrightarrow forall y in Y, exists x in X

Leftrightarrow forall x in X, exists y in Y

Leftrightarrow