The equivalence class of -2 for the relation congruence modulo 5 is о (... -11, -6, —1,4, 9, 14, ...} о (... - 12, -7, —2,3,8, 13,...} о (.. - 10, —5, —1,3, 8, 13,...} O none of the choices о (.., - 12, —7, —2,5, 8, 13, ...}

Q: 6. Let S be a set and suppose is a relation on S. For each of the following, provide a…

A: Let us solve the given problems on relation in the next steps.

Q: the set {a, b, c, d} that is (a) [BB] reflexive and symmetric (b) not symmetric and not…

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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: Is the relation of “mapping” between two sets used to determine cardinality - and not used to…

A: Note- Since you have asked multiple question, we will solve the first question for you. If you want…

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) How many elements are there in S/ ~ ? Equivalently, how man equivalence classes are there in S?…

A: This is a question of relation.

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. 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: 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: Equivalence relations "are" partitions. Let S be a set, and RC S × S be an equivalence relation on…

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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: The relation R on the set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) is defined by R= {(x,y) E AXA: xmod…

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Q: A = {x € Z: xis even} {91'SI'ZI'6'S'E} = 5 23242+3 2184 21+ 122198 th

A: Given,            To find the value of

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: 9. E is the binary relation defined on Z as follows: For all m, n E Z, m Enm-n is even. Is this an…

A: Equivalence relation

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

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Q: Prove that the relation ∼ between sets is symmetric and transitive.

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Q: Find the Car D={a, b, c, d, ..., z), n(D)=? U=universal set n(U')=? B={p people in the USA | p is a…

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Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. the equivalence…

A: The objective of the question is to understand how the equivalence classes for the given equivalence…

Q: 3. Which of the following best characterizes the statements A) The relation "divides" on the set of…

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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: tence or two what is wrong with the follo Let~ be a relation on a set S. If ~is reflexive. ~ is…

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