   Chapter 7.2, Problem 27ES ### 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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# Let D be the set of all set of all finite subsets of positive integers, and define T : Z + → D by the following rule: For every integer n , T ( n ) = the set of all of the positive divisors of n. Is T one-to-one? Prove or give a counterexample. Is T onto? Prove a give counterexample.

To determine

(a)

To check:

Whether T is one-to-one or not.

Explanation

Given information:

Consider D be the set of all finite subsets of positive integers, and T:+D is defined by the rule: For all integers n,T(n)= the set of all of the positive divisors of n.

Concept used:

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

Calculation:

Claim: T is a one-to-one function.

For this consider x,y+ and xy. Without loss of generality assume that x<y

To determine

(b)

To check:

Whether T is onto or not.

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