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) E 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 ad- ditional 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).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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) E 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 ad-
ditional 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).
Transcribed Image Text: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) E 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 ad- ditional 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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