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Let A={x,y} and let S be the set of all strings over A . Define a relationC from S to S as follows: For all strings s and t in S , (s,t)∈Cmeans thatt=ys⁢.Then C is a function because every string in S consists entirely of x ’s andy ’s and adding an additional y on the left creates a single new string that consists of x ’s and y ’s and is, therefore, also in S . Find C(x) andC(yyxyx) .

Let A={x,y} and let S be the set of all strings over A . Define a relationC from S to S as follows: For all strings s and t in S , (s,t)∈Cmeans thatt=ys⁢.Then C is a function because every string in S consists entirely of x ’s andy ’s and adding an additional y on the left creates a single new string that consists of x ’s and y ’s and is, therefore, also in S . Find C(x) andC(yyxyx) .

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 18E: Let (A) be the power set of the nonempty set A, and let C denote a fixed subset of A. Define R on...
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Question

Let 
A
=
{
x
,
y
}
 and let 
S
 be the set of all strings over 
A
 . Define a relation
C
 from 
S
 to 
S
 as follows: For all strings 
s
 and 
t
 in 
S
 ,

(
s
,
t
)
∈
C
means that
t
=
ys
⁢
.
Then 
C
 is a function because every string in 
S
 consists entirely of 
x
 ’s and
y
 ’s and adding an additional 
y
 on the left creates a single new string that consists of 
x
 ’s and 
y
 ’s and is, therefore, also in 
S
 . Find 
C
(
x
)
 and
C
(
yyxyx
)
 .

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