Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal? [35], [3], [12], [0], [-2], [17], [492]

Q: Question 33 With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is…

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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: 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: 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: 1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b…

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Q: Use any of the results in this section to evaluate the given integral along the indicated closed…

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Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

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: Consider the set Z of integers and the equivalence relation ~ definel. 2 by a. Ure set- builden…

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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: For the following relations on the set of POSITIVE integers, determine if it satisfies each of the…

A: Relation is defined on positive integer m~n <=> 19 divide m-n  Since m-m=0 and 19 divide 0 so…

Q: 5. Recall that Z stands for the equivalence classes of integers modulo n. We denote the congruence…

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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: Consider the binary relation for "less than" with the symbol <. This relation does not define an…

A: Reflexive relation: A  relation S on a set A is called reflexive relation if every element of set A…