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)

Expert Solution

Colby Messinger answered 2 years ago

Let R be a relation on the set of all integers such that aRb if and...

Let R be a relation on the set of all integers such that aRb if and only if 3a − 5b is even. Tell if R is an equivalence relation. Justify your answer. (Hint: 3b − 5a = 3a − 5b + 8b − 8a)

Let R be the following relation on the set of all alive people in the world:...

Let R be the following relation on the set of all alive people in the world: x R y if and only if x and y have the same pair of biological parents. Prove that R is an equivalence relation.

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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.

Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4 a)Construct the...

Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4 a)Construct the diagraph for this relation b)show that R is an equivalence relation Part B: Now consider the relation R on A defined by aRb iff a divides b (Divides relation) c) Show that R is partial ordering d) Contruct the hasse diagram for this relation

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

Suppose we define the relation R on the set of all people by the rule "a...

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Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or...

Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) ∈ R if and only if a) a is taller than b. b) a and b were born on the same day.

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.

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