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:ℤ+×ℤ+→ℤ+ is defined as follows.

For all (n,m)∈ℤ+×ℤ+, 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:X→Y is said to be one to one if, and only if, ∀x1,x2∈X if F(x1)=F(x2), then x1=x2.

Let (n1,m1),(n2,m2)∈ℤ+×ℤ+

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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Sect-7.1 P-1TY Sect-7.1 P-2TY Sect-7.1 P-3TY Sect-7.1 P-4TY Sect-7.1 P-5TY Sect-7.1 P-6TY Sect-7.1 P-7TY Sect-7.1 P-8TY Sect-7.1 P-9TY Sect-7.1 P-1ES

Sect-7.1 P-2ES Sect-7.1 P-3ES Sect-7.1 P-4ES Sect-7.1 P-5ES Sect-7.1 P-6ES Sect-7.1 P-7ES Sect-7.1 P-8ES Sect-7.1 P-9ES Sect-7.1 P-10ES Sect-7.1 P-11ES Sect-7.1 P-12ES Sect-7.1 P-13ES Sect-7.1 P-14ES Sect-7.1 P-15ES Sect-7.1 P-16ES Sect-7.1 P-17ES Sect-7.1 P-18ES Sect-7.1 P-19ES Sect-7.1 P-20ES Sect-7.1 P-21ES Sect-7.1 P-22ES Sect-7.1 P-23ES Sect-7.1 P-24ES Sect-7.1 P-25ES Sect-7.1 P-26ES Sect-7.1 P-27ES Sect-7.1 P-28ES Sect-7.1 P-29ES Sect-7.1 P-30ES Sect-7.1 P-31ES Sect-7.1 P-32ES Sect-7.1 P-33ES Sect-7.1 P-34ES Sect-7.1 P-35ES Sect-7.1 P-36ES Sect-7.1 P-37ES Sect-7.1 P-38ES Sect-7.1 P-39ES Sect-7.1 P-40ES Sect-7.1 P-41ES Sect-7.1 P-42ES Sect-7.1 P-43ES Sect-7.1 P-44ES Sect-7.1 P-45ES Sect-7.1 P-46ES Sect-7.1 P-47ES Sect-7.1 P-48ES Sect-7.1 P-49ES Sect-7.1 P-50ES Sect-7.1 P-51ES Sect-7.1 P-52ES Sect-7.1 P-53ES Sect-7.2 P-1TY Sect-7.2 P-2TY Sect-7.2 P-3TY Sect-7.2 P-4TY Sect-7.2 P-5TY Sect-7.2 P-6TY Sect-7.2 P-7TY Sect-7.2 P-8TY Sect-7.2 P-9TY Sect-7.2 P-10TY Sect-7.2 P-11TY Sect-7.2 P-1ES Sect-7.2 P-2ES Sect-7.2 P-3ES Sect-7.2 P-4ES Sect-7.2 P-5ES Sect-7.2 P-6ES Sect-7.2 P-7ES Sect-7.2 P-8ES Sect-7.2 P-9ES Sect-7.2 P-10ES Sect-7.2 P-11ES Sect-7.2 P-12ES Sect-7.2 P-13ES Sect-7.2 P-14ES Sect-7.2 P-15ES Sect-7.2 P-16ES Sect-7.2 P-17ES Sect-7.2 P-18ES Sect-7.2 P-19ES Sect-7.2 P-20ES Sect-7.2 P-21ES Sect-7.2 P-22ES Sect-7.2 P-23ES Sect-7.2 P-24ES Sect-7.2 P-25ES Sect-7.2 P-26ES Sect-7.2 P-27ES Sect-7.2 P-28ES Sect-7.2 P-29ES Sect-7.2 P-30ES Sect-7.2 P-31ES Sect-7.2 P-32ES Sect-7.2 P-33ES Sect-7.2 P-34ES Sect-7.2 P-35ES Sect-7.2 P-36ES Sect-7.2 P-37ES Sect-7.2 P-38ES Sect-7.2 P-39ES Sect-7.2 P-40ES Sect-7.2 P-41ES Sect-7.2 P-42ES Sect-7.2 P-43ES Sect-7.2 P-44ES Sect-7.2 P-45ES Sect-7.2 P-46ES Sect-7.2 P-47ES Sect-7.2 P-48ES Sect-7.2 P-49ES Sect-7.2 P-50ES Sect-7.2 P-51ES Sect-7.2 P-52ES Sect-7.2 P-53ES Sect-7.2 P-54ES Sect-7.2 P-55ES Sect-7.2 P-56ES Sect-7.2 P-57ES Sect-7.2 P-58ES Sect-7.3 P-1TY Sect-7.3 P-2TY Sect-7.3 P-3TY Sect-7.3 P-4TY Sect-7.3 P-5TY Sect-7.3 P-1ES Sect-7.3 P-2ES Sect-7.3 P-3ES Sect-7.3 P-4ES Sect-7.3 P-5ES Sect-7.3 P-6ES Sect-7.3 P-7ES Sect-7.3 P-8ES Sect-7.3 P-9ES Sect-7.3 P-10ES Sect-7.3 P-11ES Sect-7.3 P-12ES Sect-7.3 P-13ES Sect-7.3 P-14ES Sect-7.3 P-15ES Sect-7.3 P-16ES Sect-7.3 P-17ES Sect-7.3 P-18ES Sect-7.3 P-19ES Sect-7.3 P-20ES Sect-7.3 P-21ES Sect-7.3 P-22ES Sect-7.3 P-23ES Sect-7.3 P-24ES Sect-7.3 P-25ES Sect-7.3 P-26ES Sect-7.3 P-27ES Sect-7.3 P-28ES Sect-7.3 P-29ES Sect-7.3 P-30ES Sect-7.4 P-1TY Sect-7.4 P-2TY Sect-7.4 P-3TY Sect-7.4 P-4TY Sect-7.4 P-5TY Sect-7.4 P-6TY Sect-7.4 P-7TY Sect-7.4 P-8TY Sect-7.4 P-9TY Sect-7.4 P-1ES Sect-7.4 P-2ES Sect-7.4 P-3ES Sect-7.4 P-4ES Sect-7.4 P-5ES Sect-7.4 P-6ES Sect-7.4 P-7ES Sect-7.4 P-8ES Sect-7.4 P-9ES Sect-7.4 P-10ES Sect-7.4 P-11ES Sect-7.4 P-12ES Sect-7.4 P-13ES Sect-7.4 P-14ES Sect-7.4 P-15ES Sect-7.4 P-16ES Sect-7.4 P-17ES Sect-7.4 P-18ES Sect-7.4 P-19ES Sect-7.4 P-20ES Sect-7.4 P-21ES Sect-7.4 P-22ES Sect-7.4 P-23ES Sect-7.4 P-24ES Sect-7.4 P-25ES Sect-7.4 P-26ES Sect-7.4 P-27ES Sect-7.4 P-28ES Sect-7.4 P-29ES Sect-7.4 P-30ES Sect-7.4 P-31ES Sect-7.4 P-32ES Sect-7.4 P-33ES Sect-7.4 P-34ES Sect-7.4 P-35ES Sect-7.4 P-36ES Sect-7.4 P-37ES Sect-7.4 P-38ES

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