Let A = {−2, −1, 0, 1, 2, 3, 4, 5, 6} 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: (b) Is an equivalence relation on Z? If not, is this relation reflexive, symmetric, or transitive?…

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Q: 2. Consider the relation on A = {(1,0), (-1,0), (1,3), (2, 4), (-4,-8), (3,9), (3,6)}, defined by:…

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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 ∈ A,…

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Q: Let R be the relation on the set of integers, s.t., aRb if and only if a=b or a= -b. Is R an…

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Q: Let B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…

A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}

Q: Given a non empty set X, consider P(X) which is the set of all subsets of X.      Define the…

A: The relation is defined as follows.

Q: Suppose that R is a reflexive and transitive relation on a set A. Define a new relation E on A by…

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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 A = {−6, −5, −4, −3, −2, −1, 0, 1, 2} and define a relation R on A as follows: For all m, n ∈ A,…

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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 A be a set and R be a symmetric and transitive relation on A. Prove the following statement: If…

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

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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 ∈ 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 = {1, 2, 3, 4, ..., 23} and define a relation R on A as follows: For all x, y € A, x R y =…

A: Solution is in next step

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…

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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: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

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Q: Let a relation ∼ on R2 = {(a, b): a, b ∈ R} be defined as: (a, b) ∼ (c, d) if and only if | a | + |…

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Q: Let R be the relation on A × A , where A= {1,2,3,4} that is elements of this relation are pairs of…

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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 ∈ A,…

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Q: that P ◦ Q is an equivalence relation on X iff P ◦ Q = Q ◦ P

A: Concept:

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

A: The given set A is -3,-2,-1,0,1,2,3,4,5 and relation is defined on A is  For all m,n∈A, m R…

Q: Let R be a relation on a set A. Define a relation ∼ on A as follows: for every a, b ∈ A, a ∼ b if…

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Q: Let R = { ( a,b ) | a,b ∈ Q and a − b ∈ Z } . Prove that R is an equivalence relation on Q

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Q: Subject: Set Theory

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Q: Q7. Let R be a relation on the set Z defined by the following rule: for all a, b e Z, a Rb if and…

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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: 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 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 R be a relation on A = {1,2, 5, 8} and R = {(8,5), (2, 1), (5, 5), (5, 8), (2, 2), (8, 1)}. Are…

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Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…

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: (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: 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 S = {(x, y) E R × R: y – x is an integer} a) Prove the S is an equivalence relation on R b)…

A: Given, S=x,y∈R×R: y-x is an integer

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: 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: Let A = {1, 2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that (X, Y ) ∈ R if…

A: Let A be a non empty set, A relation R on A is said to be an equivalent relation if  1) R is…

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

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Q: A relation R is defined on the set, Z, of integers by xRy if and only if x+ y 2 5. R is A reflexive…

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

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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 and x be relations on Z defined as follows: For a, be Z, a~b if and only if 2 divides a +b. •…

A: According to the given information, it is required to solve the question 10.

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: Prove that the given relation is an equivalence relation, and describe the distinct equivalence…

A: Let A is the set of all students at your college. For every x,y∈A,  xSy⇔x is the same age as y. That…

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