What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

Q: what are the steps you take to find the equivalence classes? I still don't really understand why…

A: To determine the distinct equivalence classes of the relation R defined on Z (the set of integers)…

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: Explain why each of the following binary relations on S = {1, 2, 3} is not an equivalence relation…

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Q: Assume that you know that ~ is an equivalence relation on R\ {0} defined as follows: xy > 0. Find…

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

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Q: Let~ be the equivalence relation on Z defined by a ~ y if and only if x - y is divisible by 5. How…

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Q: We have defined the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R =…

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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: 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: And what would be the 15 equivalence relations? And what does "up to isomorphism" mean?

A: Ans-In this question we have to determine   all possible equivalence relations on the set…

Q: efine the relation ~ on the set N of positive integers by a~b if and only if  a = b(10^k) for some…

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Q: Let the relation - on the natural numbers N be defined as follows: if n is even, then n ~ n + 1; if…

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Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

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Q: tiv Consider the relation defined on Z by m~n if and only if m+n is eve (a) Show that ~ is an…

A: Consider the relation ~ defined on Z by m~n if and only if m+n is even. Now, To show  Relation ~ is…

Q: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b…

A: The objective of the question is to determine which of the given relations are symmetric and…

Q: Let R be a relation on A. Then for all n ≥ 0, prove R^n is a set. (Discrete Mathematics, powers of a…

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Q: Let be the equivalence relation on Z defined by z~ y if and only if z-y is divisible by 15. Give…

A: Equivalence relation

Q: count the number of possible equivalence relations on a set of size n by providing a formula in…

A: We use the idea of partitioning to get the total number of equivalence relations.

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

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Q: Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes…

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Q: There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (1) {(0,…

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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: 1. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

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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: = 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: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

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Q: Which of the following is an equevalence relation on the set (a, b, c} 7 O (a, a), (a, b), (b, a).…

A: Option 1 is equivalence relation. Option 2 is also is an equivalence relation. Option 3 and 4 is not…

Q: (Chapter 11.4, #3) The relation relation. Sketch it, by drawing Z as a subset of the line, then…

A: The objective is to show that x≡ymod4 is an equivalence relation. To show the relation is an…

Q: How many distinct equivalence classes exist in the relation R defined as below: x Ry + 3| (2x - )

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Q: d) ((f g)| for some CEZ, for all xE Z, f(x) – g(x) = C} e) {f, 8) | f(0) = g(1) and f(1) = g(0)}

A: Part (d) From the given information: The relation is . Here, C is constant.

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: 13. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

A: The relations on 0, 1, 2, 3 are given as: (a) 0, 0, 0, 2, 2, 0, 2, 2, 2, 3, 3, 2, 3, 3 (b) 0, 0, 0,…

Q: (a) Show that the relation defined on Z by m~n if 4m +n is divisible by 5 2 is an equivalence…

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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.