Which of the following relations is transitive? Define a relation R in the natural number. Select the correct response(s): O R= {(x, y) I x + 2y = 7} R = xsy OR= {(x, y) I x + y = 8} R = {(x, y) I x – y = 4}

Q: Given R = { (x,y) ϵ R | 0 divides x (y+1) with zero remainder, x,y ϵ A } on A = {1, 2, 3, 4, 5},…

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Q: For the relation R closure of R. {(1,2), (1,4), (3,3), (4, 1)} find (i) R2 (ii) R3 and (iii)…

A: The given relation,

Q: List the ordered pairs in the relation R from A ={0,1,2,3} to B = {0,1,2,3} where (a,b) ϵ R, if and…

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Q: 1. Let R be a relation on R x R such that (*1vi)Rs02) if and only if x,yı = x2y2. (a) Is (2,3)R(1,4)…

A: A relation from a set A to B is defined as a subset of A×B. Here R is a relation on ℝ×ℝ such that…

Q: S and T are relations on the real numbers and are defined as follows: S = {(x, y)| x y} %3D What is…

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Q: 7. State the congruence relation for ABWO and AIRO. Use only the markings in the diagram. A. ASA B.…

A: As per our guidelines we are suppose  to solve only first question. Kindly repost the other question…

Q: The relation on the set of integers R {(x, y) : 5 divides a- y} is O a. an equivalence relation O b.…

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Q: 1 In the relation . If R, =1 and %3D R R R, R,%3D3, find R.

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Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: The given relation R is as follows. R=x,y∈Z×Z:x is a multiple of y If x,y∈R, we denote x related to…

Q: Which of the following relations are transitive? The relations are in bold. (Remember: A relation R…

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Q: Let R be a relation on R × R such that (,71)R¢xI2) if and only if xıyı = x2y2. -) Is (2.3)R(1,-6) a…

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Q: Given a relation from Z (positive integer) to Z (positive integer) is defined as follows: ((m, n) E…

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Q: 2 1-Find the geometric location of the relation z – 3 -ži = v2. 3

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Q: For each relation, decide whether or not that relation is reflexive, symmetric, antisymmetric or…

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Q: (i) Give an example of a relation S on A = {1,2, 3, 4} with S is reflexive, not symmetric and not…

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Q: d. {(0,0), (1,1), (1,3), (2,2), (2,3), (3,1), (3,2), (3,3)} е. {(0,0), (0,1), (0,2), (1,0), (1,1),…

A: Explanation of the answer is as follows

Q: ) 5. Determine whether the following relations are reflexive, symmetric, antisymmetric, and/or…

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Q: 4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R…

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Q: Consider the relations given below: xRy:x loves y xRy:x2y iii. xRy:x is in the same classroom with y…

A: If x = y and y = x then we can say that relation is symmetric relation.

Q: Q2. (a) Find the equivalence class [-3]5 (b) Find the ordered pairs of the relation R from the set A…

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Q: Let R be the relation, {(a, b) e N x N:a + b is odd}. Give an example that shows that R is not…

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Q: Let Y = {0, 1,2} and Z = {0, 1} and define a relation R from A to B as follows: Given any {x,…

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Q: 1. Consider the relation R1: R - R such that (r1, y1)R1 (X2, y2) if and only if both points are on…

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Q: Characterize the relations in questions 14 and 15 in terms of whether each is reflexive,…

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Q: 5. Let R be a relation on R2 defined by (w1,y1)R(x2y2) if and only if yı +x1 = y2 + x2. (a) Is R…

A: Given relation is

Q: 3. Define a relation S from R to R as follows: For all (x, y) e R xR, (x, y) eS means that x2 y. a.…

A: Given x,y∈S  Mean x≥y    x,y∈R×R

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

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Q: Suppose that R is a symmetric relation. Match the correct term with each blank space in the…

A: Suppose  that R is a symmetric relation than prove that R-1⊆R Proof: Suppose that <x,y>∈R-1.…

Q: Consider the following relation Ron R: (x, y) E R if and only if Va y E Q. What are the properties…

A: The following relation R on ℝ:x, y ∈R,if and only if x.y ∈ℚ,

Q: A relation R is called circular if (a, b) E R and (b, c) e R implies that (c, a) e R. Show that a…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve the…

Q: List the ordered pairs in the relation R from A={0,1,2,3,4} to B={0,1,2,3} where (x,y) R if only if…

A: 1. As 0≤0, 0≤1, 0≤2, 0≤3, 1≤1, 1≤2, 1≤3, 2≤2, 2≤3, 3≤3 So the ordered pairs relation is R = {(0, 0),…

Q: 4. Let the relation R = { (a, b) e Z × Z l(a + b) = 1 (mod 5) }. a. Is the relation transitive?…

A: A relation R between two sets A and B is the set of all ordered pairs a,b such that a∈A and b∈B. We…

Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on…

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Q: 3. Let S = R × R and R be the relation on S defined by (a, b)R(c, d) iff a+c=b+d. Determine whether…

A: Reflexive: (x,y) R (x,y) As x+y=x+y Symmetric : if (a,b)R(c,d) then a+b=c+d. Since c+d=a+b then…

Q: Consider the relation on Z × Z given by aRb if a < b. Is R transitive. Answer yes or no…

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Q: Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r,…

A: (a) Obtain the composite relation as follows.

Q: Coot R be the relation A = S 2, 34 S,,73 de fned the ゲ rule Cab) ER if the wlese Carbs dixindle the…

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Q: 1. List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,…

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

Q: 6. Define a relation from R to R as follows: For all (x, y) ER X R, (x, y) ER means that y = x2. a.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Let T be the relation in the set of real numbers IR defined by xTy of both xe [n, n+1] and ye[nin+1]…

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Q: 1. Let A (2,3,4) and B= (6,8,10) and define a relation R from A to B as follows: For all %3D (x, y)e…

A: Basic properties of sets and relations can be used to find the answer to this question keeping in my…

Q: The relation on the set of integers R= {(x,y):5 divides x +y} is O a. none of the choices O b.…

A: Use the relevant definitions.

Q: (a) Explain what it means for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii)…

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Q: 7b, 7c, and 7d

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Q: Define a relation on Z x Z, xRy, |x - y| < 1. Is R reflexive, symmetric, and/or transitive? Explain…

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Q: the 品|名 Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A b) as follows: For every (x,…

A: using the concept of relation ...

Q: 1. Consider the relation R1 : R2 - R² such that (r1, y1)R1 (x2, y2) if and only if both points are…

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Q: Define a relation R on Z as follows: For all integers m and n, m Rn = 5|(m² - n²). (a) Is 1 R (-4)?…

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Q: 14. The number of ordered pairs in the relation R from = {0,1,2,3,4} to B = {0,1,2,3} where (a, b) E…

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