Given a set define a relation induced by a partition of set A and that partition must consists of at least 3 subsets? Show that this relation is an equivalence relation? Also draw the digraph for this 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

Q: c) For a set X = {1,2,3, 4, 5}, let P be the partition {{1,3, 4}, {2}, {5}}. In the equivalence…

A: Q1(c) asked and answered.

Q: For each set partition P of each set X, describe the induced equivalence relation (a) X = {a, b, c,…

A: Given, For each set partition P of each set X, describe the induced equivalence relation ~p on X.

Q: (a) classes of X induced by Prove that - is an equivalence relation on X and describe the set X/ ~…

A: This is a problem of relation.

Q: A relation Ron A is an equivalence relation if it is reflexive, symmetric, and transitive. Given: A…

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Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

Q: Let = be an equivalence relation on a set A. For every element a E A, let [a] denote the equivalence…

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Q: Given a non empty set X, consider P(X) which is the set of all subsets of X.      Define the…

A: The relation is defined as follows.

Q: Draw the direction of the graph that represents the relations.

A: We need to draw the directed graph which is represented by the given relation,…

Q: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given MI conditions are met,…

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Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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Q: 1. Consider the set Z in which the relation R is defined by aRb if and only if a + 3b is divisible…

A: According to question given that Set Z in which the relation R is defined by aRbIf and only if a+3b…

Q: Let S be the set of integers. If a, b E S, define aRb if a + b is even.Prove that R is an…

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Q: Let A be a set. Define a relation on p (A) as follows: For B and C arbitrary subsets of A, B~C iff…

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Q: Let A be a set and R be a symmetric and transitive relation on A. Prove the following statement: If…

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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: n R m in Z if nm>0

A: 1) reflexive property : for all n in Z - {0}, we have, n R n because, n•n = n² > 0 But, for n = 0…

Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: let A= {a, b, c, d} and R= { (a,a), (a, c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. draw a…

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Q: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given conditions are met,…

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Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

Q: (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in…

A: Given: A is a nonempty set, and P is a partition of A. To show: The relation R is equivalence…

Q: Consider the equivalence relation on set A={a,b,c} given by R = {(a,a),(b,b),(c,c),(a,b),(b,c)} . s…

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Q: Construct the Hasse diagram for the subset relation on the set P({a,b,c}).

A: Hasse diagram for subset of given set is made below

Q: Subject: Set Theory

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Q: In each item below, verify that ~ is an equivalence relation on the given set. (a) Let S = Z x N.…

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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: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: Determine whether or not the following relations are equivalence relations on the given set. If the…

A: Let m, n, p∈ℚ Relation is m~n in ℚ if mn≥0 (i) Reflexive: Let m∈ℚ then mm=m2≥0 Therefore m~m   ∀m∈ℚ…

Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…

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Q: Question No. 5) Show that a partition of a set S determined equivalence Relation on set S. (

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Q: If {{1, 3, 5}, {2, 4}} is a partition of the set A = {1, 2, 3, 4, 5}, determine the corresponding…

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Q: Subject: Set Theory

A: • Transitive relation means that, whenever an element a is related to an element b and b is related…

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

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Q: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5],…

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Q: Use a particular counterexample to explain why R fails to be an equivalence relation is the…

A: We take counter example   9R10,10R11⇒9R  11

Q: Let A # 0 be a set. Prove that A? is an equivalence relation on A.

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Q: Let S be a set. A subset R CS×S is called a circular relation if (i) for each a E S, (a, a) E R and…

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Q: There are as many equivalence classes as there are which of the following? (Select all that apply.)

A: There are many equivalence classes.

Q: 9.42. Prove or disprove: The union of two equivalence relations a nonempty set is an equivalence…

A: We are asked to prove or disprove, the union of two equivalence relation on a non empty set is an…

Q: 1. Let X be a set, R, S C X × X binary relations on X. Prove or disprove the following. (a) If R and…

A: A relation is equivalence if it is reflexive , symmetric and transitive

Q: Determine whether or not the following relations are equivalence relations on the given set. If the…

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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. '…

Q: Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common…

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Q: Let R be an equivalence relation on A. Find the maximum number of classes R can make if JA| = 80 and…

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Q: equivalence

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

A: We have to determine whether the relation R on the set defined in the parts (a) and (b), are…

Q: Define equivalence class and partition of a relation.

A: Define equivalence class and partition of a relation.