Define a relation on Z x Z, xRy, |x - y| < 1. Is R reflexive, symmetric, and/or transitive? Explain why or why not for each property.

Q: Let R be a relation that is symmetric and antisymmetric. Show that R is transitive

A: Let R be the relation which is symmetric and Anti-symmetric.We will show that R is transitive, that…

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: 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 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: Define a relation R on Z as follows: For all integers m and n,   m R n ⇔ 5 | (m2 − n2).   Is 1 R…

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Q: Show that the relation R on a set A is symmetric if and only if R = R-, where R is the inverse…

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Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

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Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: The given relation is not an equivalence relation. First check if the relation R is reflexive.…

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: Let f : A → B be an injective function, a be an order relation on B and 3-1 = {(x, y) E A x A :…

A: An order relation means the criterion of comparison between objects, that satisfies the properties…

Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: Reflexivity: Since x≠x+2 , therefore, (x,x)∉R and hence R is not reflexive.   Symmetricity: Let…

Q: Which of the following relations is transitive? Define a relation R in the natural number. Select…

A: We have to find

Q: Let R be a relation on a set A Let R' be the relation on A defined by Graph(R') = (A × A) –…

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Q: If R is reflexive, symmetric and transitive then the relation is said to be--------

A: Any relation R on a set S is equivalent if and only if it follows the below conditions: (a) R is…

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

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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: Let the relation S defined as S = {(x,y) | y = X2 + 4x +3}. What is the domain of S?

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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: For each relation F, indicate if it is: reflexive, anti-reflexive, or neither; symmetric, anti-…

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

Q: Let A = {a, b, c}. a) Give an example of a relation on A that is reflexive and symmetric, but is not…

A: The given set be A= {a, b, c} . Reflexive relation is a relation of elements of a set A such that…

Q: Consider the relation R = {(a, b), (a, c), (c, c), (b, b), (c, b), (b, c)}. Is R reflexive,…

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Q: d) Let R be a relation on Z and x R y if x - y is even. e) Let R be a relation on N x N where (a, b)…

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Q: Q5) Let X = {a, b,c, d} and let R = { (a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (b, d), (d,…

A: Given : X = a, b, c, d R = a, a, a, b, a, c, b, a, b, b, b, c, b, d, d, d be a relation.   To show…

Q: The domain of a relation R is the set of integers. x is related to y under relation R if x 2 = y.…

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Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

A: See the detailed hand written solution below.

Q: Draw the shape of relation z - V3e Зе V3.

A: We are given the relation : z-3eiπ3=3---(1) Now, Let, z=x+iy---(2) Now, 3eiπ3=3cosπ3+i…

Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: A relation R is said to be reflexive on a set A if for all a∈A, a,a∈R A relation R is said to be…

Q: Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or…

A: The given relation R is defined as follows.

Q: Is this relation discrete or continuous? -50 -5 -5- O Discrete O Continuous

A: This relation is Discrete.

Q: Which of the following relations is an equivalence relation? [A] xRy if and only if x-y=8 [B] xRy if…

A: We have to find which relation is equivalence relation.

Q: Give an example of a relation which is (i) reflexive and transitive but not symmetric; (ii)…

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

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Q: By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is:…

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Q: 1) Let R be a relation on N × N where (a, b) R (c, d) if a ≤ c and b ≥ d

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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: Determine whether the following relations are equivalence relations. For those relations that are…

A: Consider the given relation is given as:

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: Define a relation P from R to R as follows.for all real numbers X and Y with X>0 (X,Y)€P means that…

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Q: Give an example of a relation which is a) One-one and onto b) Many - one and onto c) One-one and…

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Q: Determine whether the following relation is an equivalence relation or not. (a) G = {(x, y) |æ…

A: We have to determine whether the given relation is equivalence relation or not.

Q: Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.

A: Prime numbers less than 10 are 2,3,5,7

Q: Let ℝ denote the set of real numbers, and  β:={(x,y)∈ℝxℝ| xy≥∅} be a relation on ℝ. Which…

A: The given relation β⊂ℝ2 is: β=x,y∈ℝ×ℝ | xy≥0 The properties of a relation is: Reflexive Irreflexive…

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: cercise 2. Give an example of a relation R on A = {1,2,3} that is neither reflexive or irreflexive.

A: Given A = {1, 2, 3}

Q: Determine the domain and range of the relation R defined byR = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4,…

A: We make a table for the relation x x+5 0 5 1 6 2 7 3 8 4 9 5 10

Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

A: Given

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: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

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Q: Define a relation Pfrom R+ to R as follows: For all real numbers x and y with x> 0, (x, y)E P means…

A: Introduction: A relation is a subset of Cartesian products of two sets. In each ordered pair, there…

Q: Give an example of a relation. Which is(i) Symmetric but neither reflexive nor transitive.(ii)…

A: i. Symmetric but neither reflexive nor transitive.