r1 1 1 0- 1 0 0 c) The matrix M represents the relations R defined. = 1 1 11 the set A = {1, 2, 3, 4}. i) List the ordered pairs in the relation R. ii) Draw the graph representing the relation R. d) How many edges does a 50–regular graph with 100 vertices have"

Q: Which of the following sets in R is linearly dependent? 36- OA {(2,0, 1), (0,4, -1), (0, 5, 1)}…

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Q: For the relation R closure of R. {(1,2), (1,4), (3,3), (4, 1)} find (i) R2 (ii) R3 and (iii)…

A: The given relation,

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: 2(a) A relation R is defined on the set A={1,2,3,4} from A to A, where R' = {(1,2); (1,3); (1,4);…

A:

Q: (b) Let R = {(x, y) E R × R : 1 < ¤ < 4 or x = 6}, and S = {(x, y) E R × R : -1 < y < 1}. i. Find…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

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

A:

Q: Consider the relation R = {(a, b) | a divides b} on the set {1, 2, 3, 4, 5, 6}. i. List all the…

A: The given relation is         R={(a,b)| a divides b} so to find the ordered pairs in the relation R,…

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…

A:

Q: Let A = Z. Define R to be the relation where a-b if ab > 0. Then R is equivalence %3D relation.

A: A relation R on a non empty set A is said to be equivalence relation if R is reflexive, symmetric…

Q: 15- R {(x,y) EZ XZI(y-x) = even element} is an symmetric %3D 16- R {(x,y) EZXZI(y-x) = even element}…

A: Recall: Reflexive, symmetry and Transitivity:   Let R be a binary relation on a set A. R is…

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: 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: The relation p = ((a, b) e R x R: 1+ ab > 0} is %3D (a) reflexive, symmetric but not transitive. (b)…

A: Given relation is ρ =  a, b ∈ ℝ × ℝ : 1 + ab &gt; 0

Q: 2 1-Find the geometric location of the relation z – 3 -ži = v2. 3

A:

Q: Let R be a relation on the set {a,b, c, d} R = {(a, b), (a, c), (b, a), (d, b)} Find: 1) The…

A: According to the given information,

Q: 3. Let A, B, and C be three distinct collinear points such that AC <AB and BC < JAB. Prove that…

A: Let given points be in order A-B-C. But then AC can never be less than or equals to half of AB.…

Q: (b) Let R= {(x,y) E R × R : 1 < x < 4 or x = 6}, %3D and S = {(x, y) E R × R: –1< y < 1}. i. Find…

A:

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 over set A. Let A = {1,2, 3, 4, 5, 6} and let R = {(a, b) e A² : |a – b| > 3} a)…

A: A relation R on a set A which is a subset of  A×A is said to be reflexive if for any x∈A,x,x∈R.  A…

Q: R. I relations on A.

A:

Q: Given A = {1, 2, 3, 4} and B = {x, y, z}. Let R be the following relation from A to B: R =…

A: (b) The arrow diagram of R

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: Given, A = { 1,2,3,4 } , B = { x,y,z } Let R be the following relation from A to B: R = {…

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Q: 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…

A:

Q: Why

A: The given relation  R={(3,3),(4,4),(6,6),(7,7),(3,6),(6,3),(4,7),(7,4)}

Q: . Let X = {1,2,3, 4} and Y = {a, b, c}. Let R C X x X be a relation on X given by TRy if, and only…

A:

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: Let the set A = {2, 3, 8, 12} and the relation R defined as the following R = { (2, 2), (2, 8), (2,…

A:

Q: Given A = {1,2, 3, 4} and B = {x,y , z}. Let R be the following relation from A to B: R =…

A: The matrix represents two relations. The domain matrix will be the first element of the relation and…

Q: Let A = {1, 2, 3, 4], B = {a, b, c}, C = {x, y, z}.  Consider the relations R from A to B and S…

A:

Q: Given A = (1, 2, 3, 4) and B = (x, y, z). Let 7? be the following relation from A to B: R =…

A: To represent a relation from A to B in matrix form  is given by

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: Below are four coordinate axes for 3-space, labeled I, II, III, and IV. Which sets of axes adhere to…

A: Once the x- and y-axes are specified, they determine the line along which the z-axis should lie, but…

Q: Let A={a.b.c.d.e) and S, T, U and V relations on A where S = {(a,g), (ab), (ba), (kd), (ce), (ed),…

A:

Q: A.  Write the relation on {a, b, c, d} in matrix form. 1.  {(a, a), (a, d), (b, c), (c, d), (d, a),…

A: The matrix form of a relation is given by M=Mij , where Mij=1    if ai,bj∈R0    if ai,bj∉R Part(1)…

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

A: 11. Consider the relation on A = {1, 2, 3} represented by the matrix 111010011   (a) To determine:…

Q: Determine whether the given set in R' is linearly independent or linearly dependent. a)…

A: b. The given set is                       -1,1,2, 0,2,-1, 3,1,2, -1,-1,1 A set of vectors v1, v2,…

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: Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. Let R and T be relations from A to B with…

A: Let A=a1,a2,...,am and B=b1,b2,..,bn Let R:A→B and T:A→B are two relations. Let m and n be their…

Q: Let R be a relation on the set {a, b, c, d} R= {(a,b), (a, c), (b, a), (d, b)} Find: 1) The…

A: According to the given information,

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: (b) Let R= {(x, y) E R × R : 1 < x < 4 or x = 6}, and S = {(x,y) E R × R : –1< y < 1}. i. Find the…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

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: 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: 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: 2. Let D be the set {xEZ I 2<x<7} and relation M on D defined by: xM y→x and factor AND x< y. y have…

A: Note:- As per our guidelines, we can answer the first three sub-parts of this problem. Please…

Q: 0 0 represents the relations R defined on 1 1 c) The matrix M = 1 11 the set A = {1, 2, 3, 4}. i)…

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Q: [1 1 01 1 c) represents the relations R defined 1 The matrix M %3| 11 1. the set A = {1, 2, 3, 4}.…

A: c) we are given that the matrix M is  1110010000111001 which represents the relations R defined on…

Q: A4. a. Draw a Digraph represented by the adjacency matrix 1 1 1 1 1 b. Consider the recurrent…

A: