In 9-33 determine whether the given relation is reflexive, sym- metric, transitive, or none of these. Justify your answers. 19. Define a relation I on R as follows: For all real numbers x and y, x I y x – y is irrational.

Q: Discrete math.  Let S = R. On S we define the relation R as follows (∀x)(∀y)(xRy ⇔ y ≥ x + 3). Is R…

A: The given set S=ℝ. The relation R defined in the set S is ∀x∀yxRy⇔y≥x+3. We have to check whether…

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: Let R= {(x,y)|x e R#, y € R#,y > x² R = {(x, y)|x € R#,y € R#,y<x+ 2} Note that R and R' are both…

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Q: (b) Let R = {(x, y) E R × R : 1 < ¤ < 4 or x = 6}, and S = {(x, y) E R × R : -1 < y < 1}. i. Find…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

Q: 1. The following subsets A, B, and C of R XR are relations on R. Sketch the set. (i) B = {(x, y):…

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Q: Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

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Q: R.2. Consider the relation R=- ={x,y):x.yeR&]x=}<3}. Is R an equivalence relation on set of real…

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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: 2. Let R be the relation on the set A = (1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) e R if the…

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Q: (b) Let R= {(x,y) E R × R : 1 < x < 4 or x = 6}, %3D and S = {(x, y) E R × R: –1< y < 1}. i. Find…

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Q: (a) Consider the set A = {x² E Q1x ER}. Determine whether A is closed under addition and…

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Q: Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric?

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Q: IS a function.. (b) Let R= {(x,y) € R × R : 1 < ¤ < 4 or x = 6}, %3D and S = {(x, y) E R × R : –1 <…

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Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

Q: Determine whether the relation R on the set of all real numbers is reflexive, symmetric,…

A: Consider the relation  for  Reflexive: For   Thus,  is not reflexive. Symmetric: For  but…

Q: II.5 Determine whether relation R on the set of all real numbers is reflexive, symmetric,…

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Q: Define the relation R on set A as follows: xR y if and only if { x, y} C A or {x, y} c A, or {x,y} <…

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Q: Let X = {x € Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y + 1 < 15}. Define a relation R from X to…

A: A relation defines the relationship between sets of values of ordered Paris. The set of elements in…

Q: Let R be a relation on the set of all functions from Z to Z defined by: R = {(f,9)|f(1) = g(3) or…

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Q: Let R be a relation on Z given by aRb if and only if a = b². Is this relation a function? Justify…

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Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b}.…

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Q: When you are rounding numbers to the nearest hundred, what is the greatest number that ran

A: When you are rounding numbers to the nearest hundred, what is the greatest number that rounds to…

Q: Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one…

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Q: 4. Define a relation R on the x-y plane as follows: Given two points (X₁,Y₁) and (x2,Y2) in the x-y…

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Q: A relation R on a set A is called irreflexive iff (Vx E A)((x, x) ¢ R). It is called asymmetric iff…

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Q: 1. State the domain of this relation. * 2 -2 {x ɛR} O {x ɛ R, x + 1} O {y ɛ R} O {y ɛ R, x + 1}

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Q: 7. 5 R 3? Is 2 R 8? Is 8 R 2? Define a relation R on Z by x R y if and only if x-y ≤ 3. Is 3 R 5? Is

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Q: Which of the following relations are functions of y in terms of x? 1) 2) 3) 4) 5- 5+ 5+ 4- 3- 2- 2-…

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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 &lt;x,y&gt;∈R-1.…

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2,…

A: The relation ≺ is defined as follows:  x1,y1≺x2,y2 if and only if x1&lt;x2 or x1=x2 and y1≤y2

Q: B Let A = {(x,y) |x-yeQ for x, y = R} be a relation on K. Which statement best describes problem?…

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Q: Define a relation R on the x-y plane as follows: Given two points (x1 ,y1) and (x2 ,y2) in the x-y…

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Q: The relation R = {(x, y): x + y s 2x} is defined on the set of integers. Which of th %3D following…

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Q: Let R = {(0, 0), (1, 1), (-1, -1)} be a relation on set A. Deduce the rule between x and y for order…

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