What is the reflexive closure of the relation R = {(a, b) | a > b} on the set of integers? Select one: a. R= {(a, b) | a > b} b. A= {(a, a) | a e A} R= {(a, b) | a > b} d. R= {(a, b) | a s b}

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: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)…

A: It is given that, A is the set of all students of a boys school.Show that R is an empty…

Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: Let R be a relation from N to N defined by R = {(a, b) : a, b ∈N and a = b2}. Arethe following…

A: Let R be a relation from N to N defined by R = {(a, b) : a, b ∈N and a = b2} (i) But Therefore,

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: Suppose that R1 and R2 are symmetric relations on a set A. a) Is R1 U R2 also reflexive? Is R1 ∩ R2…

A: Let A be any set with  symmetric relations R1 and R2 defined on it. Hence R1 and R2 be subset of…

Q: Give an example of a relation on the set {a, b, c, d} which is symmetric and transitive, but not…

A: Any relation R from a set Ato A is reflexive if and only if for every x∈A , the pair (x,x)∈R Any…

Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: we have given a set  A = { 1, 2, 3, 4}  and R is a relation on the set A where R is defined as (a,…

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

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Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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

A: By definition of  relation it is define as A relation is symmetric if and only if (b, a) ∈ R…

Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

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Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R reflexive?…

A: In this question we have to explain Is the given relation is reflexive.

Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

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: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: What is the domain of the relation x(x-3) ? {(X,y): y = (x+4)(x-7)). ) {x: x = R, x -4, x > 7} ) {x:…

A: Domain of function f(x) is the set of value of x for which f(x) is defined.

Q: Define a relation R on Z as follows: For all integers m and n, m R n 5| (m² – n²). a. Is 1 R (–9)?…

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Q: а. {(0,0), (1,1), (2,2), (3,3)} b. {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)} с. {(0,0),…

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

A: Given R be the relation, {(a, b) ∈ N x N:a + b is odd}.  We find an example that shows that R is not…

Q: Construct a relation on the set {1,2,3,4} that is reflexive, antisym- metric, and not transitive.

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

A: This relation is Discrete.

Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

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Q: A relation R is defined on the sets of integers by aRba2+b2=(a+b)2-2ab Show that R is symmetric

A: A relation is called symmetric if aRb⇔a2+b2=(a+b)2-2ab

Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: Reflexive relations: If a,a∈R for all a∈A then is reflexive relations . Symmetric relations: If…

Q: Check the following relation R on the set A = {1,2,3, 4} is reflexive, symmetric and or transitive…

A: Relation R on set A = {1, 2, 3, 4} and R is defined as, a,b ∈ R if and only if a≠b,∀a,b∈A.

Q: Let A = {1, 2, 3, 4, 5} and R be the relation defined by R = {(1,1), (2,2), (2,4), (2,5),…

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Q: Determine if the relation defines y as a ône-to

A: The given graph is: To determine if it is one-to-one.

Q: Let R be relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) e R…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Consider the relation R = {(1, 2), (2, 1), (2, 3), (3, 4), (4, 1)} on {1, 2, 3, 4}. Is R…

A: Definitions: Suppose R is relation defined on a set X then  i) R is reflexive if xRx, ∀x∈X. ii) R is…

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: Check the following relation R on the set A = {1, 2, 3, 4]} is reflexive, symmetric and or…

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Q: Given the relation R on the set of all integers defined by the rule (x, y) ER if and only if x 2 y².…

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Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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Q: Let RC R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given problem is :

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: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: Given problem is :

Q: Define a relation ~ on the set of real numbers by X~ y means | x |+|y|=|x+y|. Determine whether - is…

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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: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

Q: 3. Let R be the relation defined by x R y + x² <y? Determine ifR is an order relation on N? on Z?…

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Q: Let be the relation on True False N defined by R={(n, m) : m³ = n + 1). Then R is one-to-one.

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

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