   Chapter 7.3, Problem 22ES ### 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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# If f : X → Y and g : Y → Z are functions and g ∘ f is onto, must g be onto? Prove or give a counterexample.

To determine

To check:

If f:XY and g:YZ are two functions and gf is onto, then whether g must be onto or not.

Explanation

Given information:

f:XY and g:YZ are two functions.

Concept used:

A function is said to be onto function if each element in co-domain is mapped with atleast one element in domain.

Calculation:

Consider that gf is onto, where f:XY and g:YZ are two functions.

The objective is to show that g is onto.

Since gf:XZ is onto, so for zZ,xX such that gf(x)=z

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