Proposition 2.12. Suppose- that R is an equivalence relation on a set A, and let a, b e A. Then the following are equivalent. (i) a ~b (i) a E (b) (iii) [a] n (b] + 0 (iv) [a] = [b]

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

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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: 7 Part 3 of 4 ! Required information NOTE: This is a multi-part question. Once an answer is…

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Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: Define a relation D on the set of real of numbers as follows: Vx, y ≤ R, x Dy x-y is irrational OD…

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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: (c) Consider the equivalence relation R on the set X = {1,2,3,4,5,6,7} given by R = {(1,1),(1,6),…

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Q: 17. Equivalence relations 1. Let X = {a, b, c, d, e, f} and R be the relation on X defined by R =…

A: The given relation is an equivalence relation. The equivalence classes are given below.

Q: 3) a) Suppose A = {0,1,2,3,4} and R = {(0,0). (0,4).(1.1), (1,3).(2,2).(3,1).(3,3),(4,0).(4,4)} is…

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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: Let A = {1,2,3,4,5,6}, and consider the following equivalence relation on A: R = {(1, 1), (2, 2),…

A: Given that A= { 1 , 2 , 3 , 4 , 5 , 6} And the equivalence relation on A R = { (1,1) ,(2,2) ,(3,3)…

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: 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…