Determine whether the relations represented by the directedgraphs shown below are reflexive,symmetric, anti-symmetric, and/or transitive.

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 = {(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: A group of 4 students namely Maiyra, Bansan, Kate and Davis from final semester in Computer Sciences…

A: (i) Let R be a relation defined by R=Maiyra, DIP, Bansan, Computer Vision, Kate, DIP, Davis, Pattern…

Q: Theorem: If R is a fuzzy relation on the set X, then (R-1)-1 = R

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

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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=[n].  What are the maximium and minimum possible size of an equivalence relation on A?  Prove…

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Q: 1 1 1 0 Consider the following zero-one matrix representing a relation on the ordered set {a, b, c,…

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

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: 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: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: ) Every continuous map RP2 → S² is homotopic to the constant map.

A:

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>12

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: 1. Suppose that the matrix representation of a relation is given by 11 1 1 0 1 1 1 0 0 11 0 0 0 1 MR…

A: A zero-one matrix is the matrix representation of a relation. The zero-one matrix is the matrix Mij…

Q: Given the following adjacency matrix, A, for nodes a, b, c, and d, find the transitive closure of A.…

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Q: Consider a relation ~ on the set Z such that x~y if and only if x + y is even. The relation ~ is…

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

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Q: QUESTION 3 Let A = (1,2,3,4), and R= { (1,1), (2,2).(3,3). (1,3) (3,1) (2,3) (3,2). (1,2),(2,1)}. Is…

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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: Provide an example to show that connectedness is not a hereditary property.

A: A property P1 is said to be hereditary: If any topological space X inherits the property P1 and all…

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

A: There are two questions given and it is discrete math. The solution to the above questions is given…

Q: Give an example of a mathematical object that satisfies the described proper- ties or explain why…

A: Determinant

Q: Prove or disprove: If R and S are partial orderings on A, then R ∩ S is also a partial ordering on…

A: Partial order relation of intersection of two partial order set

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: Suppose that the matrix representation of a relation is given by 1 1 11 0 1 1 1 0 0 1 1 0 0 0 1 MR…

A: Given that the matrix representation of a relation is MR=1111011100110001

Q: Justify the following statement: the total degree (sum of all degrees of all vertices) of a finite…

A: Isomorphic Graphs Two graphs G1 and G2 are said to be isomorphic if − There exists a function ‘f’…

Q: [1 1 1] Consider the following zero-one matrix 0 1 1 representing a relation on the ordered set {a,…

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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: Problem 17. (a) Prove that <r is a reflexive, transitive relation on P(E*). (b) Prove that =r is an…

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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: A partial order relation is that which is A Reflexive, symmetric and transitive B Reflexive and…

A: A (non-strict) partial order is a homogeneous binary relation ≤ over a set P satisfying particular…

Q: 1. Let A = {cat,dog,bird,rat} and R be a relation on A defined by {(x,y) : x and y have at least one…

A: We have to solve given problem:

Q: 4- The orthogonal relation is A: symmetric and reflective relation B: symmetric and not reflective…

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Q: 4. Let R be a relation on the set {1,2, 3, 4} such that R = {(1, 1), (1, 3), (2, 2), (2, 3), (3,2),…

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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 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: Let G= Find all the conjugate classes of (G,.). (i.e G={1,a,b,a.b}).

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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: The system represented by the input-output relation, yln]= 2x[n]is an example for a first order…

A: Solve as below

Q: Consider the relation R = {(1,2), (2, 1), (2, 3), (3, 4), (4, 1)} on {1,2, 3, 4}. 1. Find the matrix…

A: R={(1,2),(2,1),(2,3),(3,4),(4,1)}

Q: {cat, dog, bird, rat} and R be a relation on A defined by :x and y have at least one letter in…

A: 2. a. First we now write the relation on A as form of matrix as follows which is also the adjacency…

Q: Which of the following is not a property of a partial ordering relation? O Reflexivity Symmetry…

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Q: Let R be a relation on the set of all integers such that a Rb if and only if a +b = 0. (a) Is R…

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Q: Exercise 5: A. Represent each of these relations on {1, 2, 3} with a matrix (with the elements of…

A: PART A a) { (1,1) , (1,2) , (1,3) } In the matrix form, 111213 b) { (1,2),(2,1),(2,2),(3,3)} In the…

Q: The binary relation {(1,1), (2,1), (2,2), (2,3), (3,1), (3,2)} on the set {1, 2, 3} is O reflexive,…

A: Relation