2. Define a relation on Nx N by (n, m) (p, q) Is an equivalence relation? Why? if n+q=p+m.

Q: Which of the following relations on the set A = {0, 1, 2, 3} is an equivalence relation? Check all…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b) , (a, c) , (b, c)} To obtain the…

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R.    Using…

Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

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Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9} and let R be the relation {(a,b) ! a , b} Find the smallest…

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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: 4. Let R be a relation on the set of all integers. xRy iff x - y = 3m for some integer m. Show 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: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

A: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a>c or a=c and b≥d Show…

Q: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

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Q: 9. Define a relation R on {-2,-1,0, 1, 2, 3, 4, 5, 6, 7} by a R b if and only if 3a+b is a multiple…

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Q: binary relation R is defined on the set of real numbers by xRy ⇔ lx - yl ≤ 1. Determine whether or…

A: R is not an equivalence relation. Because, R is not transitive. The Counter example is as follows…

Q: Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b),…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Show that the following is an equivalence relation: R = {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (3,…

A: Equivalence relations are a fundamental concept in mathematics that allow us to group elements of a…

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: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

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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)…

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Q: 4. For each relation R below, determine whether it is an equivalence relation on the given set A.…

A: Definition (Equivalence relation): A relation R is said to be an equivalence relation on a set A if…

Q: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

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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: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. the equivalence…

A: The objective of the question is to understand how the equivalence classes for the given equivalence…

Q: 3. For universe S = R² define relation ~ as: (a, b) ~ (c,d) ⇒ 2a-b2c - d. Prove that is an…

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

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Q: 1- show that [Am, A¹] = 0 for all m and n discuss the physical meanings of this relation. 2-…

A: As per the question we are given the following commutation operations : [Am , An] [∂/∂x , x] And…

Q: d) ((f g)| for some CEZ, for all xE Z, f(x) – g(x) = C} e) {f, 8) | f(0) = g(1) and f(1) = g(0)}

A: Part (d) From the given information: The relation is . Here, C is constant.

Q: 13. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

A: The relations on 0, 1, 2, 3 are given as: (a) 0, 0, 0, 2, 2, 0, 2, 2, 2, 3, 3, 2, 3, 3 (b) 0, 0, 0,…

Q: What is the composite

A: Let A,B and C be three sets. Suppose that R is a relation from A to B, and S is a relation from B to…

Q: Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, %3D 3),(2, 4),(4, 1),(2,…

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Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

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Q: Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

A: Given a relation, aRb⇔ab≤0. To check whether R is an equivalence relation on set ℤ. A relation is an…

Q: Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; Az : %3D %3D %3D {2,4,…

A: Let A=1,2,3,4,5,6 and 3 subsets of A. A1=1,3,5; A2=2,4,6,A3=3,6 we have a relation xRy if and only…

Q: (a) Show that the relation defined on Z by m~n if 4m +n is divisible by 5 2 is an equivalence…

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Q: P, - Solve the foilowing System of Linear equet;'on by Gaujs elimintion metlod :.. X, -X2 +3X3 =10…

A: Gauss elimination method basically convert an augumented matrix of a system of linear equations into…