The relation R on the set of all integer numbers is defined by (x, y) = R_if and only if |x| = [y]. Then, R is an equivalence relation. O True False

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: Write an equivalence relation of Set A = {1,2,3,4,5,6}

A: Set A={1,2,3,4,5,6}

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: ame programs. A = the set of all people in the Social Security database; a Rb if and only if a and b…

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Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: binary relation R is defined on the set of real numbers by xRy ⇔ lx - yl ≤ 1. Determine whether or…

A: R is not an equivalence relation. Because, R is not transitive. The Counter example is as follows…

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

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: The relation "is less than or equal to", denoted "S", is NOT an equivalence relation on the set of…

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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: 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: Suppose that the relation R is reflexive. Show that R* is reflexive.

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Q: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

A: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

Q: Define: what is an equivalence relation?

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Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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Q: Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; Az : %3D %3D %3D {2,4,…

A: Let A=1,2,3,4,5,6 and 3 subsets of A. A1=1,3,5; A2=2,4,6,A3=3,6 we have a relation xRy if and only…

Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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Q: Show that if for a relation R we know that R^2 ⊆ R, then R is transitive, and conversely.

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Q: The number of relations on the set A = {1, 2} is 256 . O True False

A: Number of relation with n elements 2n2

Q: Give examples: For each of the four relations between natural numbers x and y in the left column of…

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