   Chapter 7.2, Problem 5ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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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 ⇔ 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.

To determine

To find:

The two incorrect statements out of given five statements.

Explanation

Given information:

The given five statements are:

1. f Is onto every element in its co-domain is the image of some element in its domain.
2. f Is onto every element in its domain has a corresponding image in its co-domain.
3. f Is onto yY,3xX such that f(x)=y.
4. f Is onto xX,3yY such that f(x)=y

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