Define a relation on Z by a R b if a² = b². a. Prove that R is an equivalence relation. b. Describe the equivalence classes.

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: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

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: R.3. Consider the relation R = {(m,n):m,n E N & m|n}. Prove that R defines a partial order on the…

A: A relation R is said to be partial order on a set X if the relation is reflexive, transitive and…

Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

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

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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: Define the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

Q: Let R be a reflexive and transitive relation on A. Show that RN R¯' is an equivalence relation -1 on…

A: First let, A= set of integers. Then, let, R={(a,b):a,b in A} so,

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: 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: Let T be the relation defined by, For all a, b e Z, aTb iff a – b is odd. Is T an equivalence…

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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: (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: 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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