5) Let R be the relation on the integers where a Rb means a² = b². a) Is this an equivalence relation? Prove or disprove. b) Is this relation antisymmetric? Prove or disprove.

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Q: 9.32. A relation Ris defined on the set A = {a+bv2: a,b € Q, a + bv/2 + 0} by x R y if æ/y E Q. Show…

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Q: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

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Q: Prove that the relation of congruence is an equivalence relation.

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Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

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Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R symmetric? Is it…

A: R=1,2,2,1,2,3,3,4,4,1set=1,2,3,4

Q: 3. Let R be the relation defined on Z by aRb if and only if 5 | (4a + b). Prove that R is an…

A: We have given relation on ℤ and defined by  aRb if and only if 5|(4a+b). We can  see here for any…

Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

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Q: Let R be the relation on the all integers given by xRy iff x- y 2k for some integer k. (1) Prove…

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Q: Show that the relation R in the set A of all the books in a library of a college,given by R = {(x,…

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Q: 1. Let F be a nonempty family of transitive relations. Prove that NF is a transitive relation. Hint.…

A: Given that the F be a nonempty family of transitive relations.

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: 5. Let A=Z and R, ={(x,y):x-y is divisible by 5} be a relation on A . That is x R,y if and only if…

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Q: Let D be the relation on the natural numbers defined by the rule m divides n if and only if m does…

A: Let D be the relation on the natural number is defined by the rule m divides n if an only if m does…

Q: Let R be the relation on the set of people with doctorates such that (a, b) ER if and only if a was…

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A: Definition of - (1) A binary relation is an Equivalence Relation on a non-empty set  S  if and only…

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Q: 9.45. A relation Ris defined on Z by a Rb if 3a + 56 = 0 (mod 8). Prove that Ris an equivalence…

A: 3a + 5b ≡  0 (mod 8)

Q: Determine whether the relation R on  the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: Define a relation on Z by a R b if a² = b². a. Prove that R is an equivalence relation. b. Describe…

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Q: Let R be the relation on the set of natural numbers given by the following rule: (n,m) ∈R if and…

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Q: (2) Let R be binary relation on N defined by rRy if and only if r <y< 2r. Is R reflexive? Is R…

A: We have given that R be a binary relation on ℕdefined by xRy if and only if x≤y≤2x. Now we have to…

Q: Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal?…

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Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

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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: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

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Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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Q: Let R be a relation on Z defined by R = {(p, q) E Z × Z |p – q is a multiple of 3}. (a) Show that R…

A: Since you have asked a question having multiple subparts, we will solve the first three subparts for…

Q: Let R = {(f, g) | f(1) = g(1)} be a relation defined on the set of func- tions from Z to Z. Is R an…

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Q: Define - on Z as follows. Suppose that a ~ b if a² = b² (mod 6). Prove that - is an equivalence…

A: We need to prove 1) Reflexive 2) symmetric 3) transitive.

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A: Consider the fuzzy relation: R =10.800.10.20.810.400.900.4100010010.50.20.900.51 Fuzzy tolerance…

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A: We need to give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not…

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Q: Let Z be the set of integers and R be the relation on Z x Z defined by: Then R is (a,x)R(b, y) if…

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Q: Let R be the relation on the set N0 of natural numbers given by the following rule: (n,m)∈R(n,m)∈R…

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Q: Determine which of the folowing relations R on Z are oquivaknee relatinns. If R is not an equivakner…

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Q: Find all equivalence relations on {1,2, 3}.

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Q: Let - be a relation on N defined as: a ~b if a < (b – 1). (i) Is ~ reflexive? Prove your answer.…

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Q: Let R be the relation on the set of all people who have visited a particular Web page such that x Ry…

A: Given

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Q: Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is the…

A: Let S be a nonempty set. Consider the relation ~ on P(S)  defined by A~B if A∪Bc=S To show: "~" is…

Q: Let R be a relation on {a, b, c, d}) defined as R = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c),…

A: Concept:

Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ER…

A: A ={ (a,b) : where a and b are positive integers}  R= {(a,b) and (c,d) : a+d= b+c }  We have to…

Q: 3. Prove that a = b(mod7)is an equivalence relation by taking suitable examples.

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Q: Let R be the relation on the set of integers defined as aRb + 5a + 8b = 0 (mod 13). (a) Show that R…

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