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: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

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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: 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 = {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: A relation R is defined on the set of integers by: aRb = a + b = 2m + 1, where m is an integer. Show…

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Q: If a relation is an equivalence relation, state the set of equivalence classes.

A: For the given relations To check the properties (i) Reflexive (ii) Symmetric (iii) Transitive.

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 = {-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: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A: According to the given information it is required to check whether the given relation in each part…

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 R₁ and R₂ both be equivalence relations. Show by proof or disprove by counterex- ample the…

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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: Let U = {a, b, c, d, e}. Using a binary table define relation RCU x U such that R is symmetric but…

A: Given that, a set   , then by the Cartesian product  will be the sell of all possible ordered pairs…

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: 3. Prove or disprove each of the following properties for the relation below: reflexive, symmetric,…

A: The given relation, which is defined on the set of integers, 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,…

A: Given set is A={-7,-6,-5,-4,-3,-2,-1,0,1,2,3} Also R is an equivalence relation on A, defined as…

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

A: The objective of this question is to find the distinct equivalence classes of the relation R on set…

Q: Let R be the relation, {(a, b) e N x N:a + 26 is divisible by 3}. Give an example that shows that R…

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