(b) Let B = {r, t, s} and R2 is a relation on set defined by the following matrix [1 1 1] 0 1 0 0 0 1 (i) Draw the digraph for the relation R2. Examine all possible properties of R2. It is reflexive, symmetric or transitive? Justify your answer. (ii)

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: 1. if R and T are anti-symmetric relations on a set A then (R U T) is anti-symmetric relation on

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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: Are the relations represented by the following matrices equivalence relations? 1 0 1 0 0 10 1 10 10…

A: Introduction: Every relation has a matrix representation. When the diagonal entries of the matrix is…

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

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

Q: 6. Give an example of a relation R on A = {-1, –3, –5} such that: (a) R is both symmetric and…

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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: B and let R = {(x, y) E A x A | g(x) = g(v)}. Suppose g: A Show that R is an equivalence relation on…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: 8. Let a relation R be represented by the following matrix 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 10 1 0…

A: The given matrix for the relation R is: MR=1000001111100010110101001000110100001011010111100…

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: 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: 1- R1 = {(A, B) E P(X) × P(X)/A S B} 2- R2 = {(A, B) E P(X) × P(X)/AN B + 0} %3D

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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: 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: 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: 3(a) Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R=…

A: The objectives are: i) Deduce the matrix complementary relation MRC ii) Find the value of TCoR-1

Q: 1. Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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Q: Let R be the relation on R defined by R= {(x, y) E R × R | x² + y² = 4 or x = y²}. Answer each of…

A: Given that R be the relation on ℝ defined by,R=x,y∈ℝ×ℝx2+y2=4 or x=y2

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows:…

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Q: Let A = {1,2, 3, 4, 5,6} and R a relation on A whose MR is given below 0 100 0 1] 0 0 10 0 0 00 1 10…

A: Let R be a relation on a set A. The relation R can be represented using the matrix and the digraph.…

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: Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R= {(?,…

A: Disclaimer: Since you have  asked multiple question ,we will solve first question for you . if you…

Q: Let A = {1, 2, 3, 4} and R a relation on A whose matri: 1 0 1 0 0 1 0 1 is Mr = 0 0 1 1 0 0 1…

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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: Consider X = [1,2]? with the relation (x1, y1)~(x2, Y2) if x1Y2 = x2y1. Also define 3x g: X → [1,2]…

A: We shall solve first three subparts only as per company's guidelines. For others please post again…

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: 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: 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: [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: 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: As this is the multiple question type, only first question is to be solved according to the Bartleby…

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: Consider X = [1,2]? with the relation (x1, y1)~(x2, Y2) if x1Y2 = x2y1. Also define 3x g: X → [1,2]…

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Q: Discrete structure

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

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Q: [1 1 0] = |0 1 1 is li o 1l 1. The relation on a set represented by the matrix MR : A) Reflexive B)…

A: Since in the matrix MR all the elements in the diagonal are 1 by which the matrix MR is reflexive…

Q: Let R be a relation on the set A = {a, b, c, d} described by the matrix MR=(1 0 0 1          0 1 0…

A: We will use the given matrix to write R in the ordered pair form and then we will find domain and…

Q: 1. if R and T are anti-symmetric relations on a set A then (R U T) is anti-symmetric relation on А.

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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: RUR and RNR symmetric relations on X. are Show that R=Z xZ is an equivalence relation.

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Q: b) Let A = {1, 2, 3, 4} and R be a relation on A described by the matrix below. [1 0 0 1] 0 0 0 1 MR…

A: b) i. For the given set A and for the relation R, we have it in the form of matrices as…

Q: 11./ a) b) c) 1 1 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine…

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

A: image is attached

Q: Let R be a relation and S its reverse. Show that R is injective if and only if S is well defined,…

A: Consider the provided question, Given that, R be a relation and S its reverse. Let R is a relation…

Q: The adjacency matrix for the relation R on {v1, v2, v3, V4} is given below. 1 0 1 1 0 0 1 1 1 1 1 1…

A: Given the adjacency matrix for the relation R on the set A=v1, v2, v3, v4 as,…