   Chapter 7.2, Problem 21ES ### 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 S be the set of all string of 0’s and 1’s, and define L : S → Z negea by L ( s ) =   the   length of  s , for   every string  s   in   S . Is L one-to-one? Prove or given a counterexample. Is L onto? Prove or give a counterexample.

To determine

(a)

To check:

Whether L is one-to-one or not.

Explanation

Given information:

Consider S be the set of all strings of 0's and 1's.

L:SZnonneg is defined by, L(s)= the length of s, for all strings s in S.

Concept used:

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

Calculation:

Objective is to determine that L is one-to-one or not.

Claim: L is not one-to-one

To determine

(b)

To check:

Whether L is onto or not.

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