Let ∼be the equivalence relation on R defined by x∼y if and only if ⌊x⌋=⌊y⌋. Using interval notation, describe the equivalence class of 15

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: 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: Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural…

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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: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

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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: Let ℝ+ denote the set of positive real numbers. Define a relation E on ℝ+ as follows: a E b  if and…

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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: 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: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…

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

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Q: Define: what is an equivalence relation?

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

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Q: Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the…

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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…