Explanation Given information: f : X → Y and g : Y → Z are both one-to-one. Proof: Since f : X → Y and g : Y → Z are both one-to-one, so f ( x 1 ) = f ( x 2 ) ⇒ x 1 = x 2 ∀ x 1 , x 2 ∈ X And g ( y 1 ) = g ( y 2 ) ⇒ y 1 = y 2 ∀ y 1 , y 2 ∈ Y Let x 1 , x 2 ∈ X such that g ∘ f ( x 1 ) = g ∘ f ( x 2 ) g

3rd Edition

ISBN: 9781284056242

Author: David J. Hunter

Publisher: Jones & Bartlett Learning

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 2.3, Problem 34E

To determine

To prove:

That g∘f is one-to-one.

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Chapter 2.3, Problem 33E

Chapter 2.3, Problem 35E

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Essentials of Discrete Mathematics

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