Complete the definition of on equivalence relation by filling in the two blanks • A reation ~ on a sets is called on equivalence relation if •x ~ y =) yox, for all x, yEs 2 x~y and yz z = for all XIYIZES

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: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following: (a)…

A: 11. Let A be a nonempty set and ~be an equivalence relation on A. (b)  We know that for each a, b∈A…

Q: Let A be a set, and denote by the set of orderings of A. That is, A = {(A, <)< is an order relation…

A: The main objective is to show ~ is equivalence relation.

Q: Let~ be the equivalence relation on IR defined by ~y if and only if [x] = [y]- Using interval…

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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: PROVE THAT IF A RELATION X ON NON EMPTY SET B IS REFLEXIVE AND TRANSITIVE THEN THE RELATION X…

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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: For each of the relations ~ on the integers ~ is relation, explain your an equivalence following…

A: A relation on a set is said to be equivalence relation if it is reflexive, symmetric and transitive

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: Let ~ CX *X be an equivalence relation on a set X. For x EX define x := := {x |x E X} is a partition…

A: This is a question from Relation.

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: 2. Define the relation on S = Z by a~b + a = b mod 5. (1) Prove that is an equivalence relation. (2)…

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Q: A relation ''<'' is 1) İrreflexive. 2) Transitive. called a quasi-order on a set S if its: صواب ihi

A: We know that

Q: Let the relation non z defined by x ny if and only if 3/(x+2y) Show that n is an equivalence…

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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: ) For arbitrary m, n € N, let (m, n) denote the greatest common divisor of m and n. or example,…

A: A relation ~ on any set R is said to be equivalence iff i) R is reflexive i.e a~a for all a∈R ii)R…

Q: In each of the following cases of a set X and relation determine whether ~ is reflexive, symmetric,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Let denote an equivalence relation on a set A. Let a € A. Then for any x EA, x~a if and only if x =…

A: We have given a set A and a equivalence relation ~on A. We have to show that for  a,x∈A , x~a if and…

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: 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: 8) Let a 3-2 +45 for n-0, 1, 2, 3,... If we write an as a recursive relation, it is Hint: calculate…

A: 8) Given an=3.2n+4.5n for n=0,1,2,3,...   To Find: an as recursive relation

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

A: A relation R on a set X is a subset of X×X. That is R⊆X×X. (b). Let ≡6 and ≡10 are two subset on the…

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: Define a relation R on the set of natural numbers defined by (z, v) E R#z-yis divisible by 3. a)…

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Q: Let - be a relation on a set X defined as below. Determine whether is an equivalence relation on X…

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Q: Let e; = [0, ...,0, 1,0, . .., 0], where 1 is the ith entry. Show (a) e;A = A¡, ith row of A. (c) If…

A: Solution: Let ei=0,...,0,1,0,...,0, where 1 is the ith entry.

Q: 3.3: Is brotherOf an equivalence relation on the set of all people?? How about siblingof?, same…

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