2. For each equivalence relation below, find the requested equivalence class. a. R = { (1,1), (1, 3), (3, 1), (2, 2), (3, 3), (4, 4)} on {1,2,3,4}. Find [1]. b. R = { (1,1), (1,3), (3, 1), (2, 2), (3,3), (4, 4)} on {1,2, 3, 4}. Find [4]. c. Ris has-the-same-tens-digit-as on the set {xeZ : 100 < x < 200}. Find [132].

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: c) For a set X = {1,2,3, 4, 5}, let P be the partition {{1,3, 4}, {2}, {5}}. In the equivalence…

A: Q1(c) asked and answered.

Q: Let R and S be two equivalence relations on a nonempty set, and T their intersection. What's their…

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Q: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

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Q: Let A = {a,b, c, d, e, ƒ}, and let G and H be the following equivalence relations in A: G = IA U…

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Q: (d) Give the equivalence relation on {a, b, c, d, e} whose equivalence classes give the partition P…

A: Please note that we are allowed to answer only the first question so repost the other one.

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

A:

Q: The domain of the equivalence relation D is the set S: S = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17}…

A: The domain of the equivalence relation D is the set S: S = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17} For…

Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

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

A: Let A  = {-1,0,1}×{0,1,2,3}  i.e A=…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

A:

Q: 9.24. Let R be an equivalence relation on A = {a, b, c, d, e, f,g} such that a Rc, c Rd, d Rg and b…

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Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Q: 4. For (1, yı) and (r2,y2) in R² we set (11. yı) ~ (12. Y2) →{+ =3+ yi. (a) Show that ~ defines an…

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Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: Let A = {a, b, c, d, e, f,g, h}, and let G and H be the following equivalence relations in A: %3D G…

A: Given that A = a , b , c , d , e , f , g , h . Also,  G and H are the following equivalence…

Q: 7. Let R be the following equivalence relation on the set A = {1,2,3,4,5,6};: R = {(1,1),(1,5),…

A: Equivalence class of R= R  =a=x∈A :aRx 1=1,52=2,3,63=2,3,64=45=1,56=2,3,6

Q: Let A = {1,2,3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3.…

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Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

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: Given the relation R= {(1,1), (2.2), (3.3)(4.4), (1.2). (2.1) (3.4). (4.3)) on the set X- (1,2.3.4).…

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Q: 9. Let R be the relation defind on NxN by (m)R(m2) if and only if m1 – n1 = m2 – n2. Describe the…

A: The equivalence class of an element means a set of all those elements that are related to that…

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: A = {1,2,3} and let R = {(1,1), (2,2), (3,3), (1,2), (2,1),(2,3),(3,2)}, then R is:

A: If A = {1,2,3} and let R = {(1,1), (2,2), (3,3), (1,2), (2,1),(2,3),(3,2)}, then R is:

Q: 9.29. Let R be an equivalence relation defined on a set A containing the elements a, b, c and d.…

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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: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are…

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Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A…

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Q: Show that the relation R in the set A = {1, 2, 3, 4, 5} given byR = {(a, b) : |a – b| is even}, is…

A: Given that: A = {1, 2, 3, 4, 5} R = { (a,b) ; |a – b| is even}For any element a ∈A, we have |a -a| =…

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: 1. Show that R is an equivalence relation on P(A). 2. Set A = {1, 2, 3, 4} and B = {1, 24}.…

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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, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 diudes (x −…

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

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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: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5],…

A:

Q: Let A = {1, 2, 3,4, 5, 6} and let R be an equivalence relation on A.  Suppose that 1R2, 3R5 and 6R3.…

A: Given that A = {1, 2, 3, 4, 5, 6} R as equivalence relation on A Given conditions: 1 R 2, 3 R 5, 6 R…

Q: 4) Suppose R ={(a,b) €Z×Z:b-a is divisible by 3}, show that R is an equivalence relation on Z.…

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Q: 9.25. Let A = {1, 2, 3, 4, 5, 6}. The relation R = {(1,1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2),…

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Q: (b) By the Equivalence Relation Theorem, there is an equivalence relation R on Z50 such that P is…

A: A relation from X to X is called a relation in X.  If R is in X and: xRx ∀x ∈ X ⇒ R is refelexive…

Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

Q: Let I be the set of equivalence classes as defined as above. Define O as follows: if A and B are…

A: The multiplication for: Take, . Then,

Q: (b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations…

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Q: (5) Let A={-2,-1,0,1,2}. R is an equivalence relation defined as: for all x,y E A, xRy 2| (x-y?).…

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Q: Suppose an equivalence relation R has the following equivalence classes that partition the set X.…

A: The ordered pairs in the equivalence relations produced by the given partitions {0, 2}, {1}, {3, 4}.…

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,