Question

In: Advanced Math

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)

Solutions

Expert Solution


Related Solutions

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...
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...
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.
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: “(x​1,​ y​1)​...
Let A = R x R, and let a relation S be defined as: “(x​1,​ y​1)​ S (x​2,​ y​2)​ ⬄ points (x​1,​ y​1)​ and (x​2,​ y​2)​are 5 units apart.” Determine whether S is reflexive, symmetric, or transitive. If the answer is “yes,” give a justification (full proof is not needed); if the answer is “no” you ​must​ give a counterexample.
Let A = Σ*, and let R be the relation "shorter than." Determine whether or not...
Let A = Σ*, and let R be the relation "shorter than." Determine whether or not the given relation R, on the set A, is reflexive, symmetric, antisymmetric, or transitive.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT