   Chapter 7.2, Problem 31ES ### 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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# De?ne F :   Z + × Z + → Z + and G :   Z + × Z + → Z + as follows: For each ( n ,   m ) ∈ Z + × Z + , F ( n ,   m ) = 3 n 5 m and G ( n ,   m ) = 3 n 5 m .a. Is F one-to-one? Prove or give a counterexample. b. 1s G one-to-one? Prove or give a counterexample.

To determine

(a)

To check:

Whether F is one-to-one or not.

Explanation

Given information:

The function F:+×++ is defined as follows.

For all (n,m)+×+,F(n,m)=3n5m.

Concept used:

In one-to-one function, distinct elements in domain are mapped with distinct elements in co-domain.

Calculation:

The objective is to check if the function F is one-to-one.

One-to-one function: A function F:XY is said to be one to one if, and only if, x1,x2X if F(x1)=F(x2), then x1=x2.

Let (n1,m1),(n2,m2)+×+

Let F(n1,m1)=F(n2,m2), check if (n1,m1)=(n2,m2)

To determine

(b)

To check:

Whether G is one-to-one or not.

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