5. Let X be the set of all subsets of Z. Define a relation R on X as follows: Given two subsets of integers A and B, ARB if and only if An BC = Ø. Is R an equivalence relation? Prove or disprove.

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

Q: Let T: R* - R be the linear transformation represented by T(x) = Ax, where 1 -2 1 0 A = 0 1 2 4 0 0…

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Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: The given relation R is as follows. R=x,y∈Z×Z:x is a multiple of y If x,y∈R, we denote x related to…

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: 4. Let R be a relation on the set of all integers. xRy iff x - y = 3m for some integer m. Show that…

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Q: Determine whether or not the relation R on the set of all people is reflexive, netric,…

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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: 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: 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: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: Let C be a relation defined on the set of all geometric polygons, defined by any two polygons in the…

A: The given problem is from relation on sets. Here. Give that C be a relation defined on the set of…

Q: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

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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: Côñšidéř thé rélátión S on the set {a, 0, C} given by S = { (a, a), (a, b), (b, a), (b, b), (c, c),…

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Q: 3. Let X be a set and S and R equivalence relations on X. Prove or give a concrete counter example…

A: Since you have asked multiple questions, we will solve the first and second question for you. If you…

Q: 6. (a, b), C

A: Let R be the relation on the set of ordered pairs of positive integers such that a,b,c,d∈R if and…

Q: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…

A: The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…