Let A = {1, 2, 3, 4, 6, 12, 24} and R be a relation on A such that xRy if and only if x divides y. Find the matrix of the relation R. (i) Show that R is a partial order on A.Draw the digraph of R follow by its Hasse diagram.Determine least upper bound of {2, 3}. Determine the greatest lower bound of {4, 6}.

Q: Consider the matrix representing a relation R on the set {x, y, z}. 0 1 0 1 0 1 1 0 1 List…

A: To list the pairs in the relation.

Q: Let R be a partial order on P. (a) Prove: R-1 is a partial order on P. (b) How can you get the…

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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: 1. Suppose the relation R on {1, 2, 3, 4, 5} defined by (x, y) E R, if x² sy+20 (a) Write the…

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

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: 11. ( a) b) c) ) Consider the relation on A={1,2,3) represented by the matrix Determine if the…

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Q: Let A = follows: For V(a,b), (c,d) = A x A, (a,b)R(c,d) ⇒ a ≤ c and b ≤ d {0,1,2} and the partial…

A: a. The Hasse diagram is shown below.

Q: Let R be a relation on the set A = {0, 1, 4, 8} defined by xRy if and only if x + y < 8. (i) List…

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Q: 1 0 10 1 0 1 0 1 0 Let A = {1,2,3,4,5} and M, = 1 1 1 1 1 0 1 0 1 0 |1 0 1 0 1 a) Give the relation…

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Q: Given a relation, R on A = {a, b, c, d} on as follows: R = {(а, а), (а, b), (а, d), (b, b), (b, с),…

A: Relation as a Matrix: Let A = {a1,a2,a3,.......am} and B = {b1,b2,b3......bn} are two finite sets,…

Q: Let A= {1, 2, 3, 4} and let the relation R on A be defined by the matrix [1110 0101 MR then which of…

A: Given that A=1,2,3,4. The adjacency matrix of the vertices in A is given by the relation R as…

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 A = {2, 3, 4, 5, 6, 7, 8} and define a relation T on A as follows. For every x, y Е А, хТу —31(х…

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Q: Determine if each relation R is a partial order on the given set A. If it is a partial order, is it…

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

Q: b) Check whether the relation R on the set S = {1, 2, 3} with the the matrix 1 1 1 0 1 1 1 1 1 is an…

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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: Let A = {2, 4, 5}, and let R be the relation on A consisting of pairs of the form (a, b), where ab…

A: Pairs in R is: {(4,4),(4,5),(5,4),(5,5)} Only these have ab&gt;12

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: a) A computer program consists of five modules Ml, M2, M3, M4, and M5. A relation R on the set of…

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Q: 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…

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Q: The universal relation A x A on A is an equivalence relation anti-symmetric a partial ordering…

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Q: a) A computer program consists of five modules M1, M2, M3, M4, and M5. A relation R on the set of…

A: From the relation matrix for R we observe that…

Q: A. Let R be a relation on set A. A={x : x ∊ J and 0 ≤ x ≤ 12},  and R={(a,b) :  a - b  is multiple…

A: Since not particular question asked ,as per guidelines solution to only first question (i.e A) is…

Q: Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for  the…

A: Given a relation R on the set B as "is factor of" B=1,2,3,6. a The ordered pair is…

Q: 1. Let A = {2, 3, 4, 5, 6, 7, 8) and R a relation over A. Draw the directed graph and the binary…

A: The solution is given by using the definition of matrix representation and directed graph of the…

Q: Consider the Hasse diagram of the following partial order relation P: a b d. f g a) How many maximal…

A: We will be solving Q.3 part (c) and (d) as mentioned. The given Hass diagram of partial order…

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: Let < be a partially order on a set A. Show that there exists a linear order 3 on A such that if a…

A: Given that ≤ is a partial order on a set A. The objective is to show that there exists a linear…

Q: Let A = {1,2,3,4} and R a relation on A whose matrix [1 0 1 1 0 1 is MR 1 0 1 1 1 1 1 Determine…

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Q: Let A = {a, b, c, d, e,f} and P be the relation on A defined by the matrix given below. [1 0 0 1 1…

A: The relation P is given by…

Q: The matrix representation for the relation R on {v1, v2, v3, v4} is given below. The first…

A: We will use the concept of adjacency matrix to write the ordered pairs of the given matrix

Q: Consider the Hasse diagram of the following partial order relation P: a C f a) How many maximal…

A: A Hasse diagram is a graphical representation of the relation of elements of a partially ordered…

Q: Let A = {1,2, 3,4} and R a relation on A whose matrix is MR = [1 0 1 1 %3D 0 10 1 0 0 1 0 10 1 1 1…

A: Given-  A=1,2,3,4 Relation R on A whose matrix is MR=1011010100101011

Q: (a) Consider coordinates in the XY-plane, (x, y) with x, y ≥ 0 and a binary relation where (x1, y₁)…

A: Given: Consider coordinates in the XY-plane, x,y with x,y≥0 and a binary relation ≺ where…

Q: Let D30 (1,2,3,5,6, 10, 15, 30), and define a partial order on Dao by x ≤ y if 1 and only if a…

A: Given:   D30 = {1,2,3,5,6,10,15,30}

Q: 3.7 Consider a fuzzy relation R CAXA where A = {a, b, c}. R a b e 1 1 1 1 1 1 d 1 1 1 a) Determine…

A: Solution :-

Q: Given X = {1,3,5}. R is a relation on X, defined by aR,b if and only if la – bl is an even integer.…

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Q: Discrete structure

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Q: Determine whether the relation with the directed graph shown is an equivalence relation. Determine…

A: Let R be the given relation shown in the directed graph  A = {a,b,c,d} R be relation on A

Q: Let P=[[a.b,d).[c.f).le.g]] be a partition. Write the relation matrix for the implied equivalence…

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Q: Let A = {1,2, 3,4} and R a relation on A whose matrix 1 1 1 1 1 1 is Mr = 1 1 1 1 1 Determine…

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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: Let R3 be the relation on Z+ such that xR3y if and only if 2x – 3y > 0. (Recall that Z+ = {1,2,3, 4,…

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Q: Let A = {0,1,2} and the partial order relation R be defined on the set of A × A as follows: For…

A: Given- Let A = 0, 1, 2 and the partial order relation R be defined on the set of A × A as follows:…

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: 11. ( a) b) c) ) Consider the relation on 4= {1,2,3) represented by the matrix 0 Determine if the…

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Q: A. Let R be a relation on set A. A={x : x ∊ J and 0 ≤ x ≤ 12}, and R={(a,b) : a - b is multiple of 4…

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Q: 2.4 (34). Let R be a partial order relation on a finite set S. Show that S has a maximal element…

A: Given: Let R be a partial order relation on the finite set S