(a) Show that the relation defined on Z by m~n if 4m +n is divisible by 5 2 is an equivalence relation. (b) Show that the relation defined on Z by m~n if 5m +n is divisible by 4 is not an equivalence relation. 2

Q: The relation on the real numbers R defined by a ~ b if both a > b and b>a is not an equivalence…

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Q: Prove that the relation of congruence is an equivalence relation.

A: A relation is said to be an equivalence relation if and only if the relation is reflexive, symmetric…

Q: The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1,…

A: Infinite sets can also be grouped into equivalence classes, such that all the sets in a given…

Q: 2 Explain why the relation on N defined as is not an equivalence relation. {(x,y): +y is a multiple…

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Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

Q: Given the relation R = {(1,2),(2,3)} on the set A = {1,2,3} . What is the minimum  number of ordered…

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Q: Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b),…

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Q: (2.3) Prove that R is an equivalence relation.

A: Prove R is an equivalnce relation.

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

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

Q: Let the relation R defined on the set of positive integers as (x, y) ER if 3 divides X - y Determine…

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Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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Q: Give an example of relation on {1,2,3,4} that is reflexive, not symmetric, and not transitive

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: 10. (a) Find all partitions of the set {3,5). (b) For each partition P that you found in (a), find…

A: A partition of a set X is a collection of non-empty( not all subsets are empty) subsets of X such…

Q: The relation R on the set of all integer numbers is defined by (x, y) = R_if and only if |x| = [y].…

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Q: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…

Q: Give examples of relations R and S on Z such that (a) Both R and S are not equivalence relations but…

A: (a) Let R and S be two relations on ℤ such that both R and S are not equivalence relations. Let…