   Chapter 7.2, Problem 22ES ### 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 strings of 0’s and 1’s, and define D : S → Z as follows: For every s ∈ S , D ( s ) =   the   number of 1's in  s  minus the number of 0's in  s . Is D one −to-one ? Prove or give a counterexample. Is D one-to-one? Prove or give a counterexample.

To determine

(a)

To check:

Whether D is one-to-one or not.

Explanation

Given information:

Consider S be the set of all strings of 0's and 1's, and D:SZ is defined as follows:

For all sS,D(s)= the number of 1's in s minus the number of 0'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 D is one-to-one or not.

Claim: D is not one to one.

For this consider the counter example in which s1=1,s2=110

To determine

(b)

To check:

Whether D is onto or not.

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