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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 if every element in its co-domain is the image of some element in its domain.

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

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

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

E. \( f \) is onto if the range of \( f \) is the same as the co-domain of \( f \).

Answer :

The statements b and d are incorrect to express the fact that a function f is onto.

A function is a relation from A to B with the condition that for every element in the domain, there exists a unique image in the codomain (this is really two conditions: existence of an image and uniqueness of an image). We denote it f(x) , which is pronounced as “ f of x .”

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

This statement is incorrect.

d. f is onto V x E X,3y EY such that f (x)-y e. f is onto the range of f is the same as the co-domain of f.

This statement in incorrect.

To learn more about domain check the link below:

https://brainly.com/question/2264373

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