H 22. D is the relation defined on Z as follows: For all m, n = Z, m Dn ⇒ 3/(m²-n²).

Q: Determine if the relation ? = {(f, g)|f(x) = g(x) for some x ∈ ℝ} on the set of all functions from ℝ…

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Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Q: (a) Give an example of a relation on the set {a, b, c, d] which is symmetric and transitive, but not…

A: (a) Given set is: a, b, c, d. To Do: We have to give an example of a relation on the given set a, b,…

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: 1. In the diagram below, there are 9 points and 8 lines: (a) Let be the relation between the points…

A: Given, In the diagram below, there are 9 points and 8 lines. a) Let ⋄ be the relation between the…

Q: consider the relation R on R, where R = {(a, b) | a ≤ b+1}. (a) Is the relation R reflexive,…

A: i.Let  then So the relation  holds for all .So  is reflexive.ii.Since the relation is reflexive so…

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: Prove that if R is an equivalence relation on a set A, then the inverse relation R−1 is an…

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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: 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: = Give an example of an equivalence relation R on the set A {a, b, c, d, e, f, g, h} such that there…

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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: What is the significance of the line above the 'a' variable in this context?

A: Given . is nothing but a element of A.And the set is just denoted by, is called the class of . It…

Q: Indicate which of the following relations is an equivalence relation or is a partial order relation.…

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Q: Please answer the part (B). I have got a solution for the question on this platform but the answer…

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Q: R is a relation on set of integers (Z) and it is given by Then, R is (x, y) = R⇒ |x − y| ≤ 1.…

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Q: 3. Let X be a set and S and R equivalence relations on X. Prove or give a concrete counter example…

A: Since you have asked multiple questions, we will solve the first and second question for you. If you…

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

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Q: Consider the relation R on R given by R = {(a, b) | a−b > 3 or a−b = 0}. (a) Show that R is not an…

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