Consider the relation R = {(a,b) | a is congruent to b mod 3} on set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the equivalence classes of R? O (1, 4, 7, 10}, (2, 5, 8), (3, 6, 9} O {1, 2, 4, 5, 7, 8, 10}, {3, 6, 9} O {1, 5, 9}, (2, 6, 10}, {3, 7}, {4, 8} O {2, 4, 6, 8, 10}, {1, 3, 5, 7, 9}

Q: 2. Consider the relation on A = {(1,0), (-1,0), (1,3), (2, 4), (-4,-8), (3,9), (3,6)}, defined by:…

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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: Consider the set A = {2, 3, 5, 11, 12, 13} and the relation Va, b E A, a R b → a = b mod 3. List all…

A: Given the set, A=2, 3, 5, 11, 12, 13 and the relation ∀a,b∈A, a R b↔a≡b mod 3

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

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: Let A = {82,95, 146, 153, 158, 166, 180, 187, 207} and R be an equivalence relation defined on A…

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Q: Let Z be the set of integers. Consider R = {(r, y) e Z x Z: 7 divides x-y} CZ x Z. Show that R is an…

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Q: Let Z be the set of integers. Consider R = {(x, y) e Z × Z: 7 divides x-y}C Z × Z. Show that R is an…

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Q: SULU Let R be a relation over the integers (Z). Prove that R= {(a,b) : a mod 4 = b mod 4} is an…

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Q: Need help trying to solve this

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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: (b) Let R be the equivalence relation on the set S = {1,3, 5, 7, ..., 49} defined by x Ry if and…

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Q: Draw the directed graph of the relation R on A = {1,2,3,4,5,6,7,8} defined as R = {(a,b)|a,b e A and…

A: Here, the relation is: R=(a,b)|a,b∈A and a≡b mod 3 That is: a-b is divisible by 3. So, 7-1=6 is…

Q: {0,1,2,3,4,5,6,7,8,9} by x ~y A x2 = is an equivalence relation on X and identify the equivalence…

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Q: Let Z be the set of integers. Consider R = {(x, y) e Z x Z: 7 divides x-y} S Z x Z. Show that R is…

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Q: R is the congruence modulo 7 relation on Z: For all m, n E Z, mRn iff 7|(m – n). (i) Is the relation…

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Q: Define a relation R on Z by declaring that xRy if and only if x^2 =y^2 (mod4). Prove that R is…

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Q: Let R be an equivalence relation on A = {3, 4, 6, 7,8, 9} and R = {(8,3), (3, 8), (8, 8), (3, 3),…

A: Equivalence class: Consider an equivalence relation R on a set A. The equivalence class of an…

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: Let R be the relation on the set N0 of natural numbers given by the following rule: (n,m)∈R if and…

A: Definition of - (1) A binary relation is an Equivalence Relation on a non-empty set  S  if and only…

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…

A: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The equivalence…

Q: 7. Recall that, for n e Z, n > 0, there is a relation on Z called congruence mod n. The b (i.e.…

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Q: Consider the relation R on the set A = {-6, –2,0,1, 4, 5, 6, 7, 15}, defined according to the…

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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: For each of the following relations on a set {1, 2,3,4}, decide whether it is reflexive, whether it…

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Q: 5. Let A = {41, 49, 67, 71, 73, 76, 81, 88, 111} and R be an equivalence relation defined on A where…

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Q: Let R be a congruence relation modulo 7 on Z. Then the equivalence class : to which of the…

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Q: Let R be the relation on the set of natural numbers given by the following rule: (n,m) ∈R if and…

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Q: Define a relation R on the set of all integers Z as follows: for all integers m and n, m R n → m = n…

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Q: Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal?…

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Q: Let ~ be defined on the set X = {0,1,2,3,4,5,6,7,8,9} by x ~ y + x2 = y? mod 5. Prove that is an…

A: Equivalence relation are those which are reflexive symmetric and transitive

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: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

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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: on K³defined by: (a, b, c) ~ (d, e, f) if and only if ak e K – {0} such that (a, b, c) = k(c, e, d)…

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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 be the relation "congruence modulo 5" defined on Z as follows: x is congruent to y modulo 5 if…

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Q: a. Prove that the intersection of two equivalence relations on a nonempty set is an equivalence…

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Q: 3) Let S be the equivalence relation on P({0, 1, 2, 3}) defined by XSY if and only if ged(X], 4) =…

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Q: Let A = {55, 63, 70, 83, 86, 106, 113, 116, 151} and R be an equivalence relation defined on A where…

A: Given : A=55, 63, 70, 83, 86, 106, 113, 116, 151 and R is an equivalence relation defined on A where…

Q: Let A = {-5, -4, −2, 0, 3, 6, 8), and define an equivalence relation R on A as follows: (x, y) E R…

A: Let A = {-5, -4, -2, 0, 3, 6, 8}, and define an equivalence relation R on A as follows: (x, y) in  R…

Q: Let z be the set of integers and R be the equivalence relation on ZxZ defined by: (a.b)R(c.d) if and…

A: Given that R is a relation on Z×Z defined by (a,b) R(c,d) if and only if a+d=b+c.

Q: Let R be an equivalence relation on A = {0, 7, 8, 9} and R = {(7,8), (8,9), (9, 9), (7, 7), (8, 8),…

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Q: (c) Let ~ be a relation defined on Z by a R b if and only if a’ = b³ (mod 4) . Determine the…

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Q: Let R be a congruence relation modulo 7 on Z. Then the equivalence class [110] equals to which of…

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Q: , Let Z be the set of integers. Consider R = {(x, y) e Z x Z: 7 divides x-y} Z x Z. Show that R is…

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Q: Define a relation R on the integers Z saying that (m, n) is in R if m2 is equivalent to n2 (mod 7).…

A: First to prove the relation, R, on set of integers Z is equivalence relation. R is defined as:

Q: Let R be the relation "congruence modulo 7" defined on Z as follows: x is congruent to y modulo 7 if…

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Q: Let R be an equivalence relation on A = {0, 1, 5, 6, 8, 9} and R = {(6, 1), (1,6), (6,6), (1, 1),…

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Q: Let R be the relation on the set of integers defined as aRb + 5a + 8b = 0 (mod 13). (a) Show that R…

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