Let A = {82,95, 146, 153, 158, 166, 180, 187, 207} and R be an equivalence relation defined on A where aRb if and only if a = b mod 7. Show the partition of A defined by the equivalence classes of R.

Q: Define the following infinite collection of subsets of the positive integers: A1 = {x|x E Z* and 0 <…

A: A relation R is said to be an equivalence relation, if it is  Reflexive : For every a∈R→(a,a)∈R…

Q: ~ Define an equivalence relation on Z by a b if a - b is even. Show that . equivalence relation.…

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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: Let A = {74, 77, 83, 89, 92, 112, 119, 134, 148} and R be an equivalence relation defined on A where…

A: Given A={74,77,83,89,92,112,119,134,148} For a∈A  class of a=[a]={x∈A : xRa }={ x∈A : x≡a mod 5 } ={…

Q: 8) Let A = {2,3,4, 5}, R is defined on A such that (aRB) if and only if (a2 +B+a) is an even number.…

A: Given A={2,3,4,5} We define a relation R on A by (αRβ) if and only if (α2+β+a) is an even number…

Q: A relation R is defined on R by xRy if x-y e Z. Prove that R is an equivalence relation. Determine…

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Q: Let A = {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7} and define a relation R on A as follows: For all x, y EA, x…

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Q: The set {{8}, {9, 10}, {11}} is a partition of the set A. Define the equivalence relation R on the…

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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: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

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Q: A relation R is defined on Z by xRy if and only if 8 divides 3x + 5y. Prove that R is an equivalence…

A: This is a question from relation.

Q: Let S = {1;2;3;4}, and suppose that ~ is an equivalence relation on S: You are given the information…

A: Given: S=1, 2, 3, 4 and ~ is an equivalence relation on S. Also we have 1~2 and 2~3. To show: There…

Q: Define the relation on the set Z of integers by if and only if a ~b if and only if a = b + 5k for…

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Q: Consider the equivalence relation ~ on R given by a ~ b if and only if [a] = [b]. You do not need to…

A: Given that the equivalence relation ~ on ℝ defined as a~b if and only if a=b. Define a function…

Q: Show that the intersection of any collection of equivalence relations over a set A is also an…

A: We have to prove intersection of equivalence relations on a set is equivalence Let us suppose R and…

Q: 2. Suppose A = {1, 2, 3, 4, .. , 14, 15} and let R be the relation of congruence modulo 5 on the set…

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Q: Let A = {1,2,3, 4, 5, 6, 7, 8, 9, 10) and define a relation R on A by a R b if 6. and only if a and…

A: 6. By the definition, a R b iff a and b have the same remainder when divided by 4.     So, obviously…

Q: Prove that if R is an equivalence relation on a set A, then the inverse relation R−1 is an…

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Q: Show that the relation R defined on the set of integers ℤ by (a,b) Î R if a – b = 6k for some k Î ℤ…

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Q: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

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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: (a, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a),…

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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: 2. Let R be a relation defined on the set of integers Z where a Rb if and only if a? = b° (mod 5).…

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Q: Suppose 1 and ₂ are equivalence relations on a set A. Let ~ be defined by the condition that a~ b if…

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Q: Let A = {1,2,3,4,5} B= (6,7,8,9} Define an equivalence relation of p in A UB with atleast 12 members

A: A=1,2,3,4,5B=6,7,8,9A∪B=1,2,3,4,5,6,7,8,9

Q: Let A = {43, 44, 57, 67, 80, 97, 107, 109, 121} and R be an equivalence relation defined on A where…

A: Introduction: To find the partition of A defined by the equivalence classes of R, we need to find…

Q: Let A = {1,2,3,4}, and let R be a binary relation on A×A given by: ((a, b), (c, d)) ∈ R if and only…

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Q: 4. Let R be the relation on Z defined by xRy if x² = y² (mod 5). Prove that R is an equivalence…

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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: The relation defined as x ~ yx ≡ y (mod7) for x, y ∈ Z in Z Write the equivalence classes by writing…

A: Relation R is defined in Z as x≡y(mod 7)  (difference of x and y is multiple of 7) Reflexivity : For…

Q: Define the following relation R in the set X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. For integers x, y ∈…

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