   Chapter 7.2, Problem 25ES ### 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 et of all strings is a’s and b’s, and define C : S → S by    C ( s ) = a s ,                                   for     each s ∈ S . (C is called concatenation by a on the left.) Is C one-to-one? Prove or give a counterexample. Is C onto? Prove or give a counterexample.

To determine

(a)

To check:

Whether C is one-to-one or not.

Explanation

Given information:

Let S be the set of all strings in a's and b's and C:SS is defined by C(S)=as, for all sS.

( C is called concatenation by a on the left)

Concept used:

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

Calculation:

To check whether C is one-to-one function or not,

Let s1=aabb,s2=ababS

Consider,

C(s1)=C(s2

To determine

(b)

To check:

Whether C is onto or not.

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