Let R be the relation on the set A = {a1, a2, a3, a4} whose matrix is given by 1 0 1 0 0 1 0 1 1 0 1 0 1 1 (a) Show that R is an equivalence relation. (b) Find the equivalence classes determined by R.

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 R1 and R2 be relations on a set A represented by the matrices 0 1 07 1 1 1 1 0 0 0 1 = |0 1 1…

A: According to our company policy, I am supposed to answer only first three-part of the question. For…

Q: Let R1 and R2 be relations on a set A represented by the matrices 1 0 1 1 1 0 0 0 and MR, 1 MR, 1 1…

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Q: Let R, and R2 be relations on a set A represented by the matrices 1 01 1 and MR2 [1 1 01 MR. 1 1 1…

A: The matrix of the composition of relations is calculated as the productof matrices.

Q: Exercise 1. Let R = {(x, y) | x, y E Z and x + y = 0, } be a relation on Z. Prove or disprove if R…

A: Let S be a non-empty set and R be a binary relation on S. (a) The relation R is said to be reflexive…

Q: Let R1 and R2 be relations on a set A represented by the matrices ГО 1 Mr1 01 1 and Mr2 1 01 0| 1.…

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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: 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: 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: 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: 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 A = {2,3, 4, 5, 6} and define a relation R on A by %3D a Rb if and only if a and b are…

A: Consider a finite set A and let R be a relation on A. Then, the relation R can be represented…

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: 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…

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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: Name the collection of ordered pairs in the relations R on (1,2,3,4} corresponding to the matrix 1 1…

A: The given matrix is MR=1110010000111000 Write {1,2,3,4 } on top and left…

Q: A) Let A = {1,2, 3, 4} and R a relations on A whose matrices [1 1 1 1] 0 1 1 1 is MR = %3D 0 011 [o…

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

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: Let R be a relation on the set A = {1,2,3,4} defined by R = {(1,1), (1,2), (1,3), (1,4), (2,2),…

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Q: 010 = Let R₁ and R₂ be relations on a set A represented by the matrices MR₁ 1 1 1 and MR₂ = 100 ГА В…

A: Given that R1 and R2 be the relations on set A represented by the matrices…

Q: 4 - Let R be the relation on {a, b, c, d} defined by the following matrix. R is reflexive ? 1 0 1 0…

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Q: For the points (x1, y1) and (x2, y2) in the plane R?let (x1, y1)~ (x2,Y2) mean that xỉ + yỉ = x + y…

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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: Let L(x): R² → R be a mapping such that L X2 CH3 X2 then L is a linear operator. Select one: O True…

A: The given linear mapping is: L(x): ℝ2→ℝ2    such that:  Lx1x2=x2x1

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: Name the collection of ordered pairs in the relations R on {1,2,3,4} corresponding to the matrix (1…

A: Please find the detailed solution in the next step

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,…

A:

Q: Let A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using…

A: Given  A = {a, b, c, d} R = { (a, b), (b, c), (c, d), (d, b)}

Q: A. Let R be a relation on set A. A={x:xeJ and 0 SxS 12), and R={(a,b): a-b is multiple of 2)…

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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: Let R1 and R2 be relations on a set A represented by the matrices [1 1 01 [1 1 01 0| and MR, MR, Lo…

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Q: Let R be a relation on A = {1,2,3,4} such that aRb means %3D - b| < 1. Find the matrix…

A: This question is about application of linear algebra

Q: Let A = {1,2,3,4} and R and S be two relations on A whose matrices are ´1 0 0 1] [1 0 0 1] 1 0 0 1 0…

A: M

Q: Discrete structure

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Q: Exercise 4.5. Let R be a irreflexive and transitive relation on the set S. Then R is a strict linear…

A: A relation is a strict order on a set   if it is 1. Irreflexive:  (a,a) ∉ R for any . 2.…

Q: Let A be a bounded linear operator on a Hilbert space H and ||A(x)||=||x|| ¥xe H. Show that A is…

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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: 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: 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: 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: Give an example of a linear operator T on an inner product space V such that N(T) ≠ N(T∗).

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Q: Let A = {1.2. 3. 4) and R = {(1. 1). (1. 3). (2. 1). (2. 2). (2. 3). (3. 3). (4. 4)} be a relation…

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