Assume that you know that ~ is an equivalence relation on R\ {0} defined as follows: xy > 0. Find all the distinct equivalence classes of ~.

Q: Define relation R on (Z+ U {0}) × Z+ by (a, b)R(c,d) if ad = bc. Describe the equivalence class [(2,…

A: Our objective is given below:

Q: ~ Define an equivalence relation on Z by a b if a - b is even. Show that . equivalence relation.…

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Q: uts) Do the following for the set X = {1,2,3,4,5). 7. (a) Give an example of a relation on X that is…

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Q: Define a relation on R by a ~ b iff aª – b² = bª – a². (a) Show that ~ is an equivalence relation.…

A: (a). To show that the given relation is an equivalence relation, we need to show that it is…

Q: Show that “is unitarily equivalent to” is an equivalence relation on Mn×n(C).

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Q: 3. Which of the following is an equivalence relation? Explain. (a) lives in the same city as (b) is…

A: Due to Bartleby answering guidelines I have solved only question no 3. Because you didn't mention…

Q: Given two equivalence relations R and P on A. Prove that (R ∪ P) ^+ is an equivalence relation

A: Given R and P are equivalence relations.Let a∈AAs R and P are reflexive relations, hence (a,a)∈R and…

Q: A relation R is defined on R by xRy if x-y e Z. Prove that R is an equivalence relation. Determine…

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Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: Prove that the following ~ is an equivalence relation: Suppose W = (X,Y) is a graph. We define the…

A: Please see the below picture for detailed solution.

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

Q: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

Q: Let a relation ∼ on R2 = {(a, b): a, b ∈ R} be defined as: (a, b) ∼ (c, d) if and only if | a | + |…

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Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

Q: (29) Let~ be the relation on R given by y Prove that is an equivalence relation on R. Find [].…

A: A relation ~ on the set of real numbers R is defined as x~y if and only if x-y∈Z. Our aim is to show…

Q: Let S be the equivalence relation on P({1,2,3,4}) — {0} defined by XSY if and only if max(X) – |X| =…

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Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: Show that if R and R2 are equivalence relations on A, then R1 n R2 is an equivalence relation on A.

A: Equivalence relation on a set A

Q: 4. Describe all Consider the relation R on R x R defined by (x1, y1) R(x2, y2) iff x₁ - 2y2 = x₂ -…

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Q: ) Let A = {1,2,3, 4} × {1,2, 3, 4}, and define a relation R on A by (1, Yı)R(x2, Y2) if r1 + y1 = x2…

A: Equivalence relation means it should satisfy reflexive, symmetric, Transitive conditions.…

Q: Let be the equivalence relation on Z defined by z~ y if and only if z-y is divisible by 15. Give…

A: Equivalence relation

Q: 2. Let R and S be equivalence relations. Prove that RnS is an equivalence relation.

A: Let A be a non-empty set. A relation R on A is said to be equivalence relation if it is reflexive…

Q: In each of the following cases of a set X and relation determine whether ~ is reflexive, symmetric,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following:…

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Q: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

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Q: Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes…

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Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…

A: We take the help of the signum function

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: Suppose 1 and ₂ are equivalence relations on a set A. Let ~ be defined by the condition that a~ b if…

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Q: 1) Let R be the relation on Z+ such that (p, q) R(r, s) if and only if p- s = q ·r. That is, the…

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Q: (1) Show v is an equivalence relation on S. (2) Describe the equivalence classes of . (3) Describe…

A: Given: Define ~ on S=a, b: a, b∈ℤ, b≠0 by a, b~c, d if and only if ad-bc=0. To show: 1) ~ is an…

Q: F U}. Deine an equivalence relation on S by: (a, b) ~ (c, d) if and only if ad – bc = 0. (a) Show…

A: Please find the answer in next step and answer first three subparts only as per the guidelines. For…

Q: (3) Let S be the equivalence relation on {0, 1, 2,3} × {0, 1, 2} defined by (a, b)S(c, d) if and…

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Q: How many distinct equivalence classes exist in the relation R defined as below: x Ry + 3| (2x - )

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Q: Exercises 1-10, determine whether the given relation is an uivalence relation on (1, 2, 3, 4, 5). If…

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Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…

A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…