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 x- y is divisible by 5. Determine whether R is reflexive, symmetric, antisymmetric and/or transitive. Hence, state whether R is an equivalence relation, a partial order relation or neither.

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

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

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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: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: 1. This relation satisfies all the conditions of equivalence relation i.e reflexive, symmetric and…

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A: A relation is said to be an equivalence relation if and only if the relation is reflexive, symmetric…

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Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…

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Q: Consider a relation R on Z- {0} defined by the rule that (x, y) E R if and only if xy > 0. a) Prove…

A: Given the relation R on ℤ-0 defined by         x,y∈R if and only if xy>0.

Q: 1. Give and example of: (a) a binary relation that is reflexive, transitive, not symmetric and not…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A relation R is defined on Z by xRy if and only if 8 divides 3x + 5y. Prove that R is an equivalence…

A: This is a question from relation.

Q: Suppose R is both an equivalence and partial order relation. Show that every equivalence class of R…

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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: 1) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x', y')…

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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: #14

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Q: 5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R=…

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Q: 2. Define the relation on S = Z by a~b + a = b mod 5. (1) Prove that is an equivalence relation. (2)…

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Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 divdes (x –…

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

Q: Let A = {0,1,2} and r = {(0,0), (1,1), (2,2 y that r is an equivalence relation on A.

A: The relation is reflexive, since a,a∈R, where a∈A Also, since a=b where (a,b)∈R therefore, the…

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Q: Given the relation R= {(1,1), (2.2), (3.3)(4.4), (1.2). (2.1) (3.4). (4.3)) on the set X- (1,2.3.4).…

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Q: S is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, rRy if and…

A:

Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A| < [B|…

A: A partial order relation is total order relation if each of the pair of the elements are comparable.…

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A: partial order means reflexive and antisymmetric.

Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

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Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

A: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The equivalence…

Q: 3. Define the relation R on Z by mR, if and only if 2|(m – n). Show that R is an equivalence…

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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,…

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A: The given set is A=0,1,2,3,4 and the relation is defined as aRb⇔a=bc and b=ad (a) Check whether R an…

Q: 2. Let R and S be equivalence relations. Prove that RnS is an equivalence relation.

A: Let A be a non-empty set. A relation R on A is said to be equivalence relation if it is reflexive…

Q: 1. Let A & 2, 3, 4, 5, 6, 7, 83 and 9 and R a relation over A. Draw a directed graph of R after…

A:

Q: Define a relation C from R to R as follows: For any (x, y) ∈ R x R, (x, y) ∈ C means that x² + y² =…

A: (x,y) ∈ R × R (x,y) ∈ C means    x2 + y2 =4

Q: 4. For r, y E R, let z y if and only if (x- y) E Q. Show that defined as such is an equivale…

A: ~ is defined as : For all, x, y in R, x~y if and only if (x-y) belongs to Q Reflexivity : x~x for…

Q: on K³defined by: (a, b, c) ~ (d, e, f) if and only if ak e K – {0} such that (a, b, c) = k(c, e, d)…

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Q: Define a relation R on Z by xRy → x = y + 5k for k E Z. Prove that R is an equivalence relation by…

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Q: For every nonempty set A, there exists a relation R which is both an equivalence relation and a…

A: A relation R is said to be equivalence relation if R is Reflexive ,Symmetric and Transitive . R is…

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 diudes (x −…

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Q: 1 Recall that for x, y ≤ R, |x − y| ≤ Rf is the absolute value of x - y. That is, if x-y≥0 |x - y =…

A: Please see the below picture for detailed solution.

Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A]< |B|…

A: Given T be the partial order relation on P1,2,...,20 defined by ATB if and only if A&lt;B or A=B.

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…

A: Let R be a relation on a set A. Then R is said to be an equivalence relation if it is reflexive,…

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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: 1. Let A = {0,1,2,3} and R a relation over A: R = {(0,0).(0,1).(0,3).(1,1),(1,0).(2,3).(3,3)} Check…

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Q: 2. Given a relation, R on A = {a, b, c, d} on as follows: %3D R = {(a, a), (a, b), (a, d), (b, b),…

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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: (5) Let A={-2,-1,0,1,2}. R is an equivalence relation defined as: for all x,y E A, xRy 2| (x-y?).…

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Q: 1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x²…

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