Question
In: Advanced Math
Show that the given relation R is an equivalence relation on set S. Then describe the...
Show that the given relation R is an equivalence relation on set S. Then describe the equivalence class containing the given element z in S, and determine the number of distinct equivalence classes of R.
Let S be the set of all possible strings of 3 or 4 letters, let z = ABCD and define x R y to mean that x has the same first letter as y and also the same third letter as y.
Solutions
Colby Messinger answered 4 months agoRelated Solutions
Determine whether the given relation is an equivalence relation on the set. Describe the partition arising...
Determine whether the given relation is an equivalence relation
on the set. Describe the partition arising from each equivalence
relation. (c) (x1,y1)R(x2,y2) in R×R if x1∗y2 = x2∗y1.
On the set S of all real numbers, define a relation R = {(a, b):a ≤ b}. Show that R is transitive.
On the set S of all real numbers, define a relation R = {(a, b):a ≤ b}. Show that R is transitive.
Show that the relation 'a R b if and only if a−b is an even integer defined on the Z of integers is an equivalence relation.
Show that the relation 'a R b if and only if a−b is an even integer defined on the Z of integers is an equivalence relation.
Let X be a non-empty set and R⊆X × X be an equivalence relation. Prove that...
Let X be a non-empty set and R⊆X × X be an equivalence relation.
Prove that X / R is a partition of X.
Let R and S be equivalence relations on a set X. Which of the following are...
Let R and S be equivalence relations on a set X. Which of the
following are necessarily equivalence relations?
(1)R ∩ S
(2)R \ S .
Please show me the proof. Thanks!
Let R be the relation on the set of people given by aRb if a and...
Let R be the relation on the set of people given by aRb if a and
b have at least one parent in common. Is R an equivalence
relation?
(Equivalence Relations and Partitions)
Question 1. Equivalence Relation 1 Define a relation R on by iff . Prove that R...
Question 1. Equivalence Relation 1
Define a relation R on by iff .
Prove that R is an equivalence relation, that is, prove
that it is reflexive, symmetric, and transitive.
Determine the equivalence classes of this
relation.
What members are in the class [2]?
How many members do the equivalence classes have? Do
they all have the same number of members?
How many equivalence classes are there?
Question 2. Equivalence Relation 2
Consider the relation from last week defined
as:...
An equivalence relation partitions the plane R2 into the set of lines with slope 2. Describe...
An equivalence relation partitions the plane R2 into the set
of lines with slope 2. Describe
the relation on R .
let G be a simple graph. show that the relation R on the set of vertices...
let
G be a simple graph. show that the relation R on the set of
vertices of G such that URV if and only if there is an edge
associated with (u,v) is a symmetric irreflexive relation on
G
Let X be a finite set. Describe the equivalence relation having the greatest number of distinct...
Let X be a finite set. Describe the equivalence relation having
the greatest number of distinct equivalence classes, and the one
with the smallest number of equivalence classes.
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