Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A are {2, 6}, {10} and {4, 8). List all the elements in R. %3D

Q: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

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Q: Let R be the following equivalence relation on the set A = {1, 2, 3, 4, 5, 6} R= {(1, 1), (1, 5),…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

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: 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: 4. Let A = (a, b,c, d). Suppose R is an equivalence relation on A. Suppose R has three equivalence…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let Z be the set of integers. Z = (- 3, - 2, - 1, 0, 1, 2, 3 ...} Let R be an equivalence relation…

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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: (b) Let R be the equivalence relation on the set S = {1,3, 5, 7, ..., 49} defined by x Ry if and…

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Q: S and T are binary relations on the set {a, b, c, d} and are defined as follows: S%3{ (а, b), (a,…

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Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: Let S be the set of real numbers. If a, b e S, define a - b if a – b is an integer. Show that ~ is…

A: Definition of the equivalence relation helps to prove the required. A relation is said to be an…

Q: 2. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence…

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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 A={ 1, 2, 3, 4, 5} R={ (1,1), (1,2), (2,1), (2,2), (3,3), (3,4), (4,3), (4,4), (5,5) } Write the…

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Q: efine the relation ~ on the set N of positive integers by a~b if and only if  a = b(10^k) for some…

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Q: Let B= {0,1,2,3,4} and let 0} , 1,3,4|,|2} be a partition of B that induces a relation Q. Find the…

A: Consider the given information.

Q: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

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Q: Let A = {1,2,3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3.…

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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 A = {-6, –5, –1, 0, 1, 5, 6}. R is defined on A as follows: For all (m, n) E A, m Rn 5| (m² –…

A: Given: A={-6, -5, -1, 0, 1, 5, 6} and relation R is defined on A as: ∀m,n∈AmRn⇔5|m2−n2 1. To show…

Q: Let Z be the set of integers. Z = {- 3, - 2, - 1, 0, 1, 2, 3 ...} Let R be an equivalence relation…

A: I just used the definition of equivalence classes

Q: Which ONE of the following represents an equivalence relation on the set of integers? Vx.y€Z, xRy if…

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Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

A: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The 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…

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Q: (3) Let S be the equivalence relation on {0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

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Q: 1. Consider the relation R on the set A = {0,1, 2, 3, 4}, defined by: %3D aRb + a = bc and b= ad,…

A: The given set is A=0,1,2,3,4 and the relation is defined as aRb⇔a=bc and b=ad (a) Check whether R an…

Q: Show that each of the following relations equivalence classes. on Z is an equivalence relation, and…

A: In the given question we have to find the equivalence classes.

Q: 3. Let R be a relation defined on Q by: Ga) ER if ad = bc a) Show that R is an equivalence relation…

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Q: a) Let A = {4, {$}, ($, [$}}} and B = {1,2}. How many equivalence relations on A?

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Q: Let A = {a, b, c, d, e} and define an equivalence relation R C A × A on the set A as follows: R =…

A: We will answer the first question as you didn't specify any. Please resubmit the other question…

Q: Let RR be a binary relation on A={a,b,c}A={a,b,c} given by…

A: We check relationship is reflexive or not

Q: Let S = {0,±1, ±2, ±3,..., 8} and consider the relation R on S defined by (a, b) E R if and only if…

A: 1.) Reflexive : As [ a ]4 = [ a ]4 for all a in S so ( a, a ) lies in R . 2.) Symmetric : If ( a, b…

Q: Let A = {0,1, 2} × {0, 1, 2, 3}. We define an equivalence relation R on A by saying that (a, b)R(c,…

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Q: (3) Let S be the equivalence relation on {0, 1, 2,3} × {0, 1, 2} defined by (a, b)S(c, d) if and…

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Q: Let X = {1, 2, 3, 4, 5, 6}. Which of the following could be an equivalence class of an equivalence…

A: Equivalence class on a set

Q: Determine if the relation described is an equivalence relation on the given set. Let S = Z+, a ~ b…

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Q: Let L be a language. Let us define the relation R such that x Ry if for every string z we have that…

A: First to prove R is reflexive, For let consider x , then for every z  we have xz∈L↔xz∈L. Hence R is…

Q: b. Let us consider the sets A = {2,3,4,5} and B = { 0,1,2,3}. Define the relation R: A → B such that…

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Q: 4) Suppose R ={(a,b) €Z×Z:b-a is divisible by 3}, show that R is an equivalence relation on Z.…

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Q: . Draw the Hasse diagram of the relation R on A, where A = (1, 2, 3, 4}, and R = {(1, 1), (1, 2),…

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Q: Consider the equivalence relation E on N defined by Enm iff n-m is divisible by 4. Which statement…

A: An equivalence relation E is defined on the set of natural numbers N as  Enm denotes that n is…

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 = {-5, -4, −2, 0, 3, 6, 8), and define an equivalence relation R on A as follows: (x, y) E R…

A: Let A = {-5, -4, -2, 0, 3, 6, 8}, and define an equivalence relation R on A as follows: (x, y) in  R…

Q: Let z be the set of integers and R be the equivalence relation on ZxZ defined by: (a.b)R(c.d) if and…

A: Given that R is a relation on Z×Z defined by (a,b) R(c,d) if and only if a+d=b+c.

Q: Consider the relation R on the set Z defined by a R b if and only if 3|(a+2b) for a, b ∈ Z. Show…

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Q: (5) Let A={-2,-1,0,1,2}. R is an equivalence relation defined as: for all x,y E A, xRy 2| (x-y?).…

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Q: Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the…

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Q: Let R and S be equivalence relations on a set A; recall that by definition R, S ⊆ A × A. Prove that…

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