Let R be the relation on N defined by a R b if either a | 2b or b | 2a. Is R an equivalence relation?

Q: (b) Is an equivalence relation on Z? If not, is this relation reflexive, symmetric, or transitive?…

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Q: Let B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…

A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}

Q: d. Ris a relation on Z* such that (x, y) e R if and only if there is a positive integer n such that…

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Q: Let R be the relation defined on P({1, . . . , 100}) by A R B    if and only if |A ∪ B| is even.…

A: Relation on a set

Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: Let A = Z. Define R to be the relation where a-b if ab > 0. Then R is equivalence %3D relation.

A: A relation R on a non empty set A is said to be equivalence relation if R is reflexive, symmetric…

Q: Let - be the relation on R\{0} given by x ~ y if and only if xy is positive. Prove that this is an…

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Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: b. Define a relation SER XR by S ={ (x,y) E R × R |x – y € Z }. Prove that S is an equivalence…

A: By equivalence relation, we mean that the relation is reflexive, symmetric, and transitive.Here we…

Q: let R be the relation on the set A = {1, 2, 3, 4, 5, 6} defined by a R bif and only if a = 2b.

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Q: Let R be the relation defined by x R y x² < y² Determine if R is an order relation on N? on Z?…

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Q: F is the relation defined on Z as follows: Vr, n E Z, mFn =7|(m² – n²). (a). Prove that F is an…

A: Equivalence relation and classes

Q: Let D be the binary relation defined below. For all u, w e 2, u D w → w=u +7 or w= u - 7. Show…

A: Solution of given problem is as below: A binary relation is equivalance relation if it satisfies the…

Q: Show that if R and R2 are equivalence relations on A, then R1 n R2 is an equivalence relation on A.

A: Equivalence relation on a set A

Q: a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different…

A: Follow the answer below.

Q: Let R be the relation on N defined by x Ry if x and y share a common factor other than 1. Determine…

A: The relation R is defined by xRy if x and y share a common factor. We need to check reflexivity and…

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 A = {1,2,3, 4} × {1,2, 3, 4}, and define a relation R on A by (1, Yı)R(x2, Y2) if r1 + y1 = x2…

A: Equivalence relation means it should satisfy reflexive, symmetric, Transitive conditions.…

Q: Consider the binary relation R defined on (N* x N*) by: V (X1. Yı). (x2. Y2) E N* x N*, (x1. Yı) R…

A: Order relation (definition)-: A relation R is called an order relation if it is reflexive,…

Q: Let R be a relation on Z. Then Ris an equivalence relation if it is defined by xRy if and only if…

A: R is an equivalent relation iff R is reflexive. R is symmetric. R is transitive.

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

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Q: Let R1 and R2 be equivalence relations on a nonempty set A. a. Prove or disprove: R1 U R2 is an…

A: A relation defined on set A is said to be an equivalence relation, if it is: 1) Reflexive relation…

Q: Let R be the relation on the set of integers such that a R b if and only if a = b or a = - b.…

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Q: Let R be the relation on the set of real numbers such that x R y if and only if x and y are real…

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Q: Let R be the relation on N defined by x R y if x and y share a common factor other than 1. Determine…

A: The relation R is defined as xRy on natural numbers Nsuch that x and y share a common factor other…

Q: Let us consider the following relation R on the set of all pairs of integers: (a,b)R(c,d) if a = c…

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Q: Let S be the following relation on R: S = {(x, y) = R² :y-x is rational}. Prove that S is an…

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Q: 1. A relation R is defined on Z* × Z* by (m,n)R(p, q) → m+q = n + p . (a). Prove that R is an…

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Q: Let S be the following relation on ℂ: S = {(x, y) ∈ ℂ2 : y − x is real}. Prove that S is an…

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Q: A relation R is defined on R by a R b if a – b e Z. Prove that R is an equivalence relation and…

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Q: t R be the relation on the set of ordered pairs of positive integers ch that ((a,b), (c,d)) e R if…

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Q: 8. Let A = Z* U {0}, define relation R on A × Z* by (k,l)R(m,n) → kn = lm. (a). Prove that R is an…

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Q: . Let R be the relation on N defined by xR y if x and y share a common factor other than 1.…

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Q: Define a relation R on the set J ={ 0, 1, 3, 4, ,5, 6 } as follows for all x, y E J x R y if and…

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Q: Let S be the following relation on C: S = {(x, y) = C²:y-x=bi for some real number b}. Prove that S…

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Q: Let A = Z. Define R to be the relation where a~b if ab > 0. Then R is equivalence relation.

A: We have given the set A = { Z : the set of integers }  R= { (a,b) : a,b belongs to Z and a.b &gt;0}…

Q: 6. (a) Let ~ be the relation on Mat2(R) defined by: A ~ B if and only if the (2, 1) entry of A – B"…

A: This problem can be solved as follows:

Q: 5) Let R be the relation on the integers where a Rb means a² = b². a) Is this an equivalence…

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Q: Let R be the relation defined on P({1,.…, 100}) by ... ARB if and only if |AUB| is even. Is R…

A: Relation: - A subset of the productA× B could be a relation R from a non-empty set A to a non-empty…

Q: . Let R be the relation on Z→ Z such that ((a,b),(c,d)) eR = a+d =b+c. Show that R is an equivalence…

A: An equivalency relation on a set is a reflexive, symmetric, and transitive relationship for…

Q: Define a relation T on R as follows: for all x and y in R, x T y if and only if x2=y2. (a) Prove…

A: Given that a relation T on R such that for all x and y in R, xTy if and only if x2=y2 (a) We have to…

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 S be the following relation on C: S = {(x, y) = C²:y-x is real}. Prove that S is an equivalence…

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Q: 18. Let R be the relation on R defined by xRy → x – y is an integer. Prove that R is an equivalence…

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Q: Let R be the relation on Z defined by x Ry if and only if x+ 3y is even. Prove that R is an…

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Q: (a) Let R be the relation on Z defined as follows: For a, b e Z, a~b if and only if a is a multiple…

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Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

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Q: Let ∼ be the relation on Mat2(R) defined by: A ∼ B if and only if the (2, 1) entry of A − BT equals…

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