Let R be an equivalence relation on A = {a, b, c, d, e, f, g} such that aRc, cRd, dRg and bR f . If there are three distinct equivalence classes resulting from R, then determine these equivalence classes and determine all elements of R."

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: Please help me solve this prove

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Q: Let A = {2,3,4,...,17,18). Let R be the equivalence relation on AxA, defined by (a,b)R(c,d) if and…

A: Let A = {2,3,4,.......... 17,18].Let R be the equivalence relation on AXA, defined by (a,b)R(c,d) if…

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: 6. Let X = {1,2,3,4, ... ,16}. Define xRy to mean that 5 divides x - y. a) List the elements of R-1.…

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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: 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: ' (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: Find the smallest equivalence relation (namely an equivalence relation with the fewest number of…

A: Find the smallest equivalence relation such that { (a,b), (a,c), (a,d), (d,e) } is a subset of…

Q: 7. Let S = {1,2,3, ...,8}. Let R be the relation on S defined by the following: %3D xRy + xy is a…

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Q: Multiplication on the number pairs is defined as follows: (a, b) · (c, d) = (ad + bc, ac + bd).& in…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let R={ (a,a). (a,b). (b.b). (b,a). (CC). (d,d), (e,e), (f,f). (d,e), (e,d). (e,f), (f.e). (d.f).…

A: Given:  R = (a, a), (a, b), (b, b), (b, a), (c, c), (d, d), (e, e), (f, f), (d, e), (e, d), (e, f),…

Q: "Let R be the relation defined on Z by aRb if a + b is even. Show that R is an equivalence relation…

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Q: 3. On the relation R on the set {1, 2, 3, 4, 5} defined by the rule (x, y) e R if x+y<6. a) List the…

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Q: a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different…

A: Follow the answer below.

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: 1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b…

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Q: Let I be the set of all straight lines in the plane. Define and equivalence relation R by x R y iff…

A: Let, R be a relation on L(set of all straight lines in the plane) defined as, xRy iff x and y are…

Q: Given set A = {1, 2, 3} and S = P(A) The relation is defined as xRy ⇔ |x| = |y| Indicate the…

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

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Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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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: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: Let X = {1, 2, 3, 4, 5, 6}. Which of the following could be an equivalence class of an equivalence…

A: Equivalence class on a set

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,…

Q: Let A = {a, b, c, d, e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence…

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Q: Give at least three different examples of equivalence relations.   Note: In every example please…

A: A relation R on a set A is said to be an equivalence relation if and only if the relation R is…

Q: (d) Justifying your answer, find the smallest set of related pairs which must be added to R in order…

A: We know that a relation is called an equivalence relation if it is reflexive, symmetric and…

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

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Q: a. Let A = The set of numbers involve in your college ID. And R = {(x, y)1+ 2 divdes (x3 + y} be a…

A: Part (a) Write Cartesian form of set R: A=0,1,3,5,7R=x,y|⇔2 divides…

Q: Question 2 List all possible equivalence relations on the set {1,2,3,4} without repetition up to…

A: To determine: The possible equivalence relations on the set 1,2,3,4.

Q: 6. Prove the following statements and provide an illustration to substantiate the proof. a) Let R1…

A: (i), (ii) &amp; (iii) implies R1 intersection R2 is an equivalence relation.