Let A = {1, 2, 3, 5, 6, 10, 15, 30} and R be a relation on A such that aRb if and only if a is a multiple of b. Show that R is a partial order relation on A. Hence draw the Hasse diagram of the relation R on A.

Q: 8. Consider the binary relation R defined on (N* x N*) by: V (x1. Y1). (X2. Y2) E N* x N*, (x1. Yı)…

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Q: Let R be the relation on the set of integers, s.t., aRb if and only if a=b or a= -b. Is R an…

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Q: ) Let R = {(a,b) : 3keza = k * b} be a relation over the positive integers. Prove or disprove that R…

A: Given that R=(a,b):a=k*b To show reflexive it is enough to show that a~a. It is true because, a=1*a.…

Q: Let R be a relation on the set of all integers such that aRb if and only if 3a – 5b is ever 1) Is R…

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Q: Let R be a relation on the set N of positive integers defined by aRb if and only if the product axb…

A: This question is about equivalence  class .

Q: Let R be a binary relation R on Z, defined by: Vx, y € N*, x R y =3neN* such that y = x" (a) Show…

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Q: Let ρ be a relation on Z+ such that aρb if there exists an n ∈ Z such that a × 5n = b. i. Give any 3…

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Q: Let R= {(a, b): 3keza k* b} be a relation over the positive integers. Prove or disprove thatR is a…

A: A relation R is partial order relation if R is reflexive, antisymmetric and transitive.

Q: Let R be the relation on the set of ordered pairs of positive integers such that  ((?, ?), (?, ?)) ∈…

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Q: Below is the Hasse diagram for a partial order relation R on the set {a, b, c, d, e}. e d be C Are…

A: Introduction: Hasse diagram is very significant in graphing a relation. In this diagram, the…

Q: Let R be a relation on the set of all integers such that aRb if and only if a +b is even. Is R…

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Q: Let R be a relation on the set A of ordered pairs of positive integersdefined by (x, y) R (u, v) if…

A: Given:

Q: Let S ⊆ N, and for any c, d ∈ N, consider a relation R such that cRd if and only if there exists a ∈…

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Q: efine the relation ~ on the set N of positive integers by a~b if and only if  a = b(10^k) for some…

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Q: Define the relation on the set Z of integers by if and only if a ~b if and only if a = b + 5k for…

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

A: Given set is A = {1, 2, 3, 4, 5} and relation is R = {(1, 1), (1, 2), (2, 2), (2, 5), (3, 1), (3,…

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

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Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

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

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.

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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: A particular relation * is defined on the set Z-{0} by x * y if and only if every prime factor of x…

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Q: 1. Consider the relation R on the set A = {0,1, 2, 3, 4}, defined by: %3D aRb + a = bc and b= ad,…

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: 1. Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: solution

Q: Suppose R1 is a relation on domain X1 and R2 is a relation on domain X2 Define a new relation R…

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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 A × A, where A = {1,2,3,4}, that is, ele- ments of this relation are pairs…

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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: a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is an…

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Q: Define a relation on the set {a, b, c, d} that is 6. (a) irreflexive and transitive, but not…

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

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: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

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Q: Let R be the relation on the set {1, 2, 3, 4} containing the ordered pairs (1, 1), (1, 3), (1, 4),…

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Q: . Draw the Hasse diagram of the relation R on A, where A = (1, 2, 3, 4}, and R = {(1, 1), (1, 2),…

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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: 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: A relation R is defined on the set, Z, of integers by xRy if and only if x+ y 2 5. R is A reflexive…

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Q: . Determine whether or not each of the binary relations R defined on the given sets A are reflexive,…

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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: 7. Let R be a binary relation R on Z, defined by: Vx, y E N*, x R y+3N€N* such that y = x" (a) Show…

A: (a)The given relation is xRy⇔∃n∈N*  such that y=xn We will verify that R is an ordered relation on…

Q: 5. Let R be a relation defined on Z by a Rb if and only if 3 | (a + 2b). (a) Prove that R is an…

A: A relation to be an equivalence relation must satisfy the following three properties:  1. Reflexive…

Q: Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs {(0, 1), (1, 1), (1, 2),…

A: To find the transitive closure of a relation, we just add the ordered pairs that completes the…

Q: Consider the set A = {2, 3, 5, 7}. Create a relation R on A that is a partial order with at least…

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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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Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

A: Given: Let A be a non-empty set let~ be a relation on ℘(A) Let "A" be a non-empty set Let ~ be a…

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A: A partial order relation leads to poset which is very interesting.