a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different equivalence classes of a given relation R exist?

Q: Which of the following relations on the set A = {0, 1, 2, 3} is an equivalence relation? Check all…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: The relation R on the set of all integer numbers is defined by R = {(x, y) = Z × Z: x - y ≤ 2} is an…

A: Given a relation R on the set of all integer numbers defined by R={(x, y)∈Z×Z:x-y≤2}.  We have to…

Q: 2. Let R = {(x, y) = R x R = |x] + [y] =4}. Then R is a relation on R. Is R an equivalence relation…

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Q: Show that the relation R on ZxZ defined by (a, b) R (c, d) if and only if a + d = b + c is an…

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Q: 2 Explain why the relation on N defined as is not an equivalence relation. {(x,y): +y is a multiple…

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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: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

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Q: binary relation R is defined on the set of real numbers by xRy ⇔ lx - yl ≤ 1. Determine whether or…

A: R is not an equivalence relation. Because, R is not transitive. The Counter example is as follows…

Q: 1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b…

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Q: 1. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

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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 the relation R on the set Z be given by the condition: (x, y) E Rif and only if x4 = y4. Answer…

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Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: Define a relation R on the set of natural numbers defined by (z, v) E R#z-yis divisible by 3. a)…

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