Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common biological parent} Show whether or not R is an equivalence relation.

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

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Q: Let R be the relation on the set of ordered pairs of positive integers such that  ((?, ?), (?, ?)) ∈…

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Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: Let S be the set of real numbers. If a, b e S, define a - b if a – b is an integer. Show that ~ is…

A: Definition of the equivalence relation helps to prove the required. A relation is said to be an…

Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

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Q: Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b} is an…

A: Given, the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b}.

Q: 1. Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

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Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈…

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Q: Show that the intersection of any collection of equivalence relations over a set A is also an…

A: We have to prove intersection of equivalence relations on a set is equivalence Let us suppose R and…

Q: Given the relation R- {(1,1), (2.2). (3,3).(4.4), (1,2). (2,1). (3,4), (4,3)) on the set X…

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Q: (a) Show that R is an equivalence relation. (b) List three members of each of the equivalence…

A: Equivalence relation: A relation R is called an equivalence relation in a set A, if it follows the…

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

A: Here given that the set is A = {a, b, c, d} and the relation on A is given by R = {(a, c), (b, b),…

Q: Determine whether the relation R on  the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: Let R be the relation on A × A, where A = {1,2,3,4}, that is, ele- ments of this relation are pairs…

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Q: Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: Given :-

Q: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

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Q: Suppose A is a set and R is a reflexive and transitive relation on A. Show that the

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Q: Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

A: We will find whether the relation is reflexive, symmetric or transitive as following.

Q: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

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Q: Determine the following relation on the set {a, b, c, d}, is reflexive, irreflexive, symmetric,…

A: Let R represent a relation on a given set S=a,b,c,d. Then, relation R is said to be reflexive; if…

Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

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Q: For non empty binary relation R={(a, a),(a, b),(b, a),(b, b),(c, c),(c, d),(d, c),(d, d)} on the set…

A: We have to solve given problem:

Q: let R be an equivalence relation and let [x] be the equivalence class of x, prove x belong to [x]

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Q: Let R be relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) e R…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

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Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: Let us consider the following relation R on the set of all pairs of integers: (a,b)R(c,d) if a = c…

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Q: Determine if the relation described is an equivalence relation on the given set. Let S = Z+, a ~ b…

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Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered…

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Q: Let A be a set and R be a reflexive relation on A. Prove that R is an equivalence relation if and…

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Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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Q: Let A = {a, b, c, d}, and R = {(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d)} be a…

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Q: etermine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: Sketch a digraph for a relation on the set {a, b, c, d} that is irreflexive and symmetricbut not…

A: Denote R by the relation on the set S={a, b, c, d} that is irreflexive, symmetric and not…

Q: Give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not symmetric, and…

A: We need to give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not…

Q: Prove the understated statements concerning the relation &lt; on the set Z of all integers . If x…

A: To prove: If x&lt;y and y&lt;z then x&lt;z. Proof: The first inequality x&lt;y suggest that the…

Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…