Consider the following relation < over reals: x < y iff (x– y) e Z. Prove that it is an equivalence and characterize its equivalence classes

Q: Determine if the relation ? = {(f, g)|f(x) = g(x) for some x ∈ ℝ} on the set of all functions from ℝ…

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Q: Let A = { 2, 3, 4 } and B = { 6, 8, 10, 12 } and define a relation R from A to B as follows: %3D For…

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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: i Determine whether or not the relation R on the set of all real numbers is reflexive, symmetric,…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

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 a…

A: Given  Set  = set of all natural numbers N Relation = R = { (a,b) : a is multiple of b }   A…

Q: 6x + 5 Define a functionf: R* → R as follows: for all real numbers x, f(x) = Then f is both…

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Q: Let S = R^2 2 and define the relation R as follows (x1, y1)R(x2, y2) ⇔ x1^2+y1^2 = x2^2+y2^2 Show…

A: We have to check all condition of equivalent relation  i.e. reflexive , symmetric  and transitive ,…

Q: Let S be the set of all ordered pairs of non-negative integers. Let R be a relation defined on A…

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Q: For graph G below, fill in the table for the in-degree and out-degree of each vertice. 9. d f G…

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Q: Let R be a relation over the positive integers defined as follows: R = {(a,b) | 2b < a < 3b }…

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Q: 5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12,…

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Q: Determine whether the relation R is a partial order relation on the set of positive…

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Q: Discrete math Let S = R^2 and define the relation R as follows (x1, y1)R(x2, y2) ⇔ (x1)^2+(y1)^2 =…

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Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

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: Let be the equivalence relation on Z defined by z~ y if and only if z-y is divisible by 15. Give…

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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: Indicate which of the following relations is an equivalence relation or is a partial order relation.…

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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

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

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Q: 2. Let A={1, 2, 3, 4, 5, 6} and let R be a relation on A defined as follows: Va,be A, (a,b)…

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Q: (9) Consider the relation R on the set {1,2,3,4,5) given by R= {(1,1), (2, 2), (3, 2), (1, 3),…

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Q: R is a relation on set of integers (Z) and it is given by Then, R is (x, y) = R⇒ |x − y| ≤ 1.…

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Q: Define the relation R over integers as follows: R = { (a, b) | |a - b| < 5 } Determine if R is (a)…

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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: 11. ( a) b) c) [1 1 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 0 1 1…

A: 11. Consider the relation on A = {1, 2, 3} represented by the matrix 111010011   (a) To determine:…

Q: Consider the relation R on R given by R = {(a, b) | a−b > 3 or a−b = 0}. (a) Show that R is not an…

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Q: Prove or disprove if the composition of surjective relations is surjective. If it is not true, find…

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