Let S be the set of binary strings {010, 100, 110, 111,1110,01110,10111,11110,11111}. A relation R on S is defined as fol- lows: (a,b) ∈ R if and only if a ∈ S has the same number of 0’s as b ∈ S. Prove that R is an equivalence relation. Determine the partition of S that corresponds to R. (That is, determine all equivalence classes that form the partition)
Let S be the set of binary strings {010, 100, 110, 111,1110,01110,10111,11110,11111}. A relation R on S is defined as fol- lows: (a,b) ∈ R if and only if a ∈ S has the same number of 0’s as b ∈ S. Prove that R is an equivalence relation. Determine the partition of S that corresponds to R. (That is, determine all equivalence classes that form the partition)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 3TFE:
True or False
Label each of the following statements as either true or false.
If is an equivalence...
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Let S be the set of binary strings {010, 100, 110, 111,1110,01110,10111,11110,11111}. A relation R on S is defined as fol- lows: (a,b) ∈ R if and only if a ∈ S has the same number of 0’s as b ∈ S. Prove that R is an equivalence relation. Determine the partition of S that corresponds to R. (That is, determine all equivalence classes that form the partition).
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