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, mRn e 3i(m It is a fact that Ris 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 A = {2,3,4,...,17,18). Let R be the equivalence relation on AxA, defined by (a,b)R(c,d) if and…

A: Let A = {2,3,4,.......... 17,18].Let R be the equivalence relation on AXA, defined by (a,b)R(c,d) if…

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: Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have…

A: We are given that,      w1 R w2  <=> w1 and w2 have a letter in common.  Now, it is obvious…

Q: 3. Which of the following is an equivalence relation? Explain. (a) lives in the same city as (b) is…

A: Due to Bartleby answering guidelines I have solved only question no 3. Because you didn't mention…

Q: need help

A: Step 1: First find out the (m,n) which belong to the equivalence classes R for x, y ∈ A. As mRn ⟺…

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

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

A: Equivalence classes of  [a]={a}.   Since only the element "a" is in the relation with "a" .…

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: Let~ be the equivalence relation on Z defined by ~y if and only if z Give three examples of elements…

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Q: need help

A: Thus, the elements −3,0,3,6 are all related to each other, and the elements −2,−1,1,2,4,5,7 are…

Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: Suppose R, S are equivalence relations on set A. Prove or disprove that (a) R-¹nS is also an…

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Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Let A = {1,2,3, 4, 5, 6, 7, 8, 9, 10) and define a relation R on A by a R b if 6. and only if a and…

A: 6. By the definition, a R b iff a and b have the same remainder when divided by 4.     So, obviously…

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 R be a relation defined on the set of integers as follows: a R b iff 6 divides  (a - b). R is…

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Q: Prove that if R is an equivalence relation on a set A, then the inverse relation R−1 is an…

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Q: Define a binary relation on the set S=(-3, -2, -1, 1, 2, 3} as follows: R= {(a,b) ab>0} %3D a. Find…

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

A: Given a set, A=-3, -2, -1, 0, 1, 2, 3, 4, 5, 6. R be relation on A, defined by, R=x, y: 3|x-y, ∀x, y…

Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A…

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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: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

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

A: Given : A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and R is an equivalence relation on A defines as ;…

Q: Discrete Math: Lets say B = {1,2,3,4,5,6}. Let R be the smallest equivalence relation on B which…

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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