Let A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} and define a relation R on A as follows: For all x, y E A, x R y ↔ 3|(x - y). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [0] [1] = [2] = [3] = = How many distinct equivalence classes does R have? classes List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

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: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

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Q: Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have…

A: We are given that,      w1 R w2  <=> w1 and w2 have a letter in common.  Now, it is obvious…

Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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Q: Let A = {-5,-4,-3,-2,-1,0,1,2,3} and define a relation R on A as follows: For all m, n ∈ A, m R n…

A: We know that For a given set A  and an equivalence relation R on A, the equivalence class of an…

Q: 4 1) 3 bes this digraph illustrate a relation that is symmetric or transitive or neither? ymmetrid…

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Q: Let f be continuous on S(0, 1) = {z : |2| = 1}. 1. Show that f(2) -dz. f(2)dz: S(0,1) 22 Use the…

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Q: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

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Q: Let R = { ( a, b ), ( a, d ), ( b, d ), ( c, a ), ( c, c ), ( d, b ), ( d, c ) } be a relation on…

A: Given: R=a,b,a,d,b,d,c,a,c,c,d,b,d,c   The relation R2 contains all ordered pairs (x, z) if (x, y)…

Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) E…

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Q: set {(a,b),(a, a), (c, a), (b, b)} (a). Let X = {a,b,c} be sets. is a relation on X and find its…

A: Answer and explanation is given below..

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: lation. Justify why your answers are corre R is a relation on the set of all people sue R is a…

A: EQUIVALENCE RELATION: If a relation R on a set A satisfies the following three criteria, it is…

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

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Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…

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Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

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Q: Let A = {4, 5, 10, 21, 24). List the ordered pairs in the relation R = {(a, b) E AXA: alb). (Recall…

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Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

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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: By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is:…

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Q: Let A = {19, 20, 22, 23} and B= {20, 22, 24}, and let the relation R from A to B be defined by…

A: Option (b) is correct.

Q: Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3) and define a relation R on A as follows: For all x, y…

A: Given : A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and R is an equivalence relation on A defines as ;…

Q: It is based upon properties of relations. *Explanation is mandatory. Check whether the following…

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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: Let A = {0,1, 2} × {0, 1, 2, 3}. We define an equivalence relation R on A by saying that (a, b)R(c,…

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Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: Define the relation R on 72 = Z x Z by (a, b) R (c, d) if a + d = b+ c. Prove that R is ar…

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