#2. Let S be the set of all strings of O's and 1's of length 3. Define a relation R on S as follows: s R t == for all strings s and t in S, the two left-most characters of s are the same as the two left-most characters of t. Prove that R is an equivalence relation on S.
#2. Let S be the set of all strings of O's and 1's of length 3. Define a relation R on S as follows: s R t == for all strings s and t in S, the two left-most characters of s are the same as the two left-most characters of t. Prove that R is an equivalence relation on S.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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![# 2.
Let S be the set of all strings of O's and 1's of length 3. Define a relation R
on S as follows: s Rt e= for all strings s and t in S, the two left-most
characters of s are the same as the two left-most characters of t. Prove that
R is an equivalence relation on S.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd20fa932-311a-46cd-86ab-78d74c804e39%2Febd6bd59-78f0-4c15-9ca5-d50a20dfbb95%2Fb92a5z4_processed.png&w=3840&q=75)
Transcribed Image Text:# 2.
Let S be the set of all strings of O's and 1's of length 3. Define a relation R
on S as follows: s Rt e= for all strings s and t in S, the two left-most
characters of s are the same as the two left-most characters of t. Prove that
R is an equivalence relation on S.
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