Let A = {−6, −5, −4, −3, −2, −1, 0, 1, 2} and define a relation R on A as follows: For all m, n ∈ A, m R n  ⇔  5|(m2 − n2). It is a fact that R is an equivalence relation on A. Use set-roster notation to list the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

Q: Let R be a relation on the set of all integers such that aRb if and only if 3a – 5b is ever 1) Is R…

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Q: Let R be a relation on the set N of positive integers defined by aRb if and only if the product axb…

A: This question is about equivalence  class .

Q: Consider the relation K on N defined by Knm iff n <m.Which statement below is true? K is an…

A: It is Irreflexive.

Q: Let Z be the set of integers. Consider R = {(x, y) e Z × Z: 7 divides x-y}C Z × Z. Show that R is an…

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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: Let R be the relation consisting of all pairs (x, y) such that x and y are strings of uppercase and…

A: Let R be a relation on a set A R is an equivalence relation if it is reflexive, symmetric,…

Q: PROVE THAT IF A RELATION X ON NON EMPTY SET B IS REFLEXIVE AND TRANSITIVE THEN THE RELATION X…

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

A: We have to find the equivalence of the given function and we are also given with the set in which…

Q: Let A = {-5,-4,-3,-2,-1,0,1,2,3} and define a relation R on A as follows: For all m, n ∈ A, m R n…

A: We know that For a given set A  and an equivalence relation R on A, the equivalence class of an…

Q: Let A = {-3, -2, –1, 0, 1, 2, 3, 4, 5, 6, 7} and define a relation R on A as follows: For all m, n E…

A:

Q: 2. Let R₁ be a relation on the set A and R₂ be a relation on the set B. Let R be the relation…

A: A relation is a subset of Cartesian product of two sets. Therefore, every element in a relation set…

Q: Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b} is an…

A: Given, the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b}.

Q: Define the relation on the set Z of integers by if and only if a ~b if and only if a = b + 5k for…

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Q: Let R be the relation on the all integers given by xRy iff x- y 2k for some integer k. (1) Prove…

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Q: 1. Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

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Q: F is the relation defined on Z as follows: Vr, n E Z, mFn =7|(m² – n²). (a). Prove that F is an…

A: Equivalence relation and classes

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

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Q: Let R be a reflexive relation on A. Show that R" is reflexive for all positive integers n.

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Q: (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in…

A: Given: A is a nonempty set, and P is a partition of A. To show: The relation R is equivalence…

Q: Given the relation R= {(1,1), (2.2), (3.3)(4.4), (1.2). (2.1) (3.4). (4.3)) on the set X- (1,2.3.4).…

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Q: Let R be a reflexive and transitive relation on A. Show that RN R¯' is an equivalence relation -1 on…

A: First let, A= set of integers. Then, let, R={(a,b):a,b in A} so,

Q: Given the relation R- {(1,1), (2.2). (3,3).(4.4), (1,2). (2,1). (3,4), (4,3)) on the set X…

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Q: Let S' = {x € R² : ||x|| = 1} C X. and endow S' with the same equivalence (b) relation - as above.…

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Q: Let H be the set of all human beings. Consider the relation R defined on H by xRy if and only if x…

A: R defined on H by xRy if and only if x and y have the same biological mother. reflexivity : x &amp;…

Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an equivalence…

A: Given, R1 and R2 are equivalence relations in a set A. So, both R1 and R2 are Reflexive, Symmetric…

Q: Define a relation on Z by a R b if a² = b². a. Prove that R is an equivalence relation. b. Describe…

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Q: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

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Q: Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

A: We will find whether the relation is reflexive, symmetric or transitive as following.

Q: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

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Q: Let A = {-7, -6, –5, -4, –3, -2, –1, 0, 1, 2, 3} and define a relation R on A as follows: For all m,…

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Q: Let S be a set of distinct symbols. Show that the relation defined onW(S) in this chapter is an…

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Q: (a, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a),…

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Q: Define a relation Q on the set R × R as follows. For all ordered pairs (w, x) and (y, z) in R x R,…

A: The relation Q on the set R×R is defined as follows. For all ordered pairs w, x and y, z in R×R, w,…

Q: Let R be the relation on the set of integers such that a R b if and only if a = b or a = - b.…

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Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

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Q: Let A Z and let the relation R be defined on A by zRy if and only if 7 divides r-y. a) Show that R…

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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: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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Q: Let A (-4, -3, -2, -1,0, 1, 2. 3, 4, 5, 6) and define a relation R on A as follows For all m, nE A,…

A: Given A={-4,-3,-2,-1,0, 1, 2, 3, 4, 5, 6}

Q: Q1. Let A be a set of nonzero integers and let be the relation on A defined by (a, b) - (c, d)…

A: Solution:-

Q: Determine whether or not the relation R on the set of all people is reflexive,  symmetric,…

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Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

Q: Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common…

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Q: Let R be an equivalence relation on A. Find the maximum number of classes R can make if JA| = 80 and…

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Q: Let A = {-5, -4, -3, -2, -1, 0, 1, 2, 3} and define a relation R on A as follows: For all m, n e A,…

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

A: A ={ (a,b) : where a and b are positive integers}  R= {(a,b) and (c,d) : a+d= b+c }  We have to…

Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

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Q: 8. Let A be a set of nonzero integers and let R be a relation on A × A defined by (a, b)R(c, d)…

A: Equivalence relation