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 x be a set and let R be a relation on x such x is...

Let x be a set and let R be a relation on x such x is simultaneously reflexive, symmetric, and antisymmetric. Prove equivalence relation.

Let R be a relation on a set that is reflexive and symmetric but not transitive?...

Let R be a relation on a set that is reflexive and symmetric but not transitive? Let R(x) = {y : x R y}. [Note that R(x) is the same as x / R except that R is not an equivalence relation in this case.] Does the set A = {R(x) : x ∈ A} always/sometimes/never form a partition of A? Prove that your answer is correct. Do not prove by examples.

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...

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

Suppose we define the relation R on the set of all people by the rule "a R b if and only if a is Facebook friends with b." Is this relation reflexive? Is is symmetric? Is it transitive? Is it an equivalence relation? Briefly but clearly justify your answers.

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.

1. Let R be the relation on A = {1, 2, 3, 4, 5} given by...

1. Let R be the relation on A = {1, 2, 3, 4, 5} given by R = {(1, 1),(1, 3),(2, 2),(2, 4),(2, 5),(3, 1),(3, 3),(4, 2),(4, 4),(4, 5),(5, 2),(5, 4),(5, 5)}. (a) Draw the digraph which represents R. (b) Give the 0 -1 matrix of R with respect to the natural ordering. (c) Which of the five properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does R have? Give a brief reason why or why not each property holds. 2. Let...

Let S = {1,2,3,4} and let A = SxS Define a relation R on A by...

Let S = {1,2,3,4} and let A = SxS Define a relation R on A by (a,b)R(c,d) iff ad = bc Write out each equivalence class (by "write out" I mean tell me explicitly which elements of A are in each equivalence class) Hint: |A| = 16 and there are 11 equivalence classes, so there are several equivalence classes that consist of a single element of A.

Let A = R x R, and let a relation S be defined as: “(x1, y1)...

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