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), (3, 4)}. Represent R using a matrix and a directed graph.

Q: Determine whether the set in P_2 is linearly independent.    S={x^2 , +1, 2 - 1, 2}

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Q: Draw the directed graph of the relation R = {(1,2), (2,1), (1,1), (2,2), (3,3), (4,1)} X=123 43

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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: 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: 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: R, S, and T are relations defined on A {0, 1, 2, 3}. Let S = {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

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Q: Is the relation with the directed graphs shown below an equivalence relation? 4. 6.

A: Let  A be a nonempty set. A relation ~ on the set A is an equivalence relation provided that ~ is…

Q: Prove that every well order is a linear order,

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Q: Represent the relation R on (refer to image)

A: According to the given information, Relation R is defined as:

Q: Draw the directed graph of the relation R on A = {1,2,3,4,5,6,7,8} defined as R = {(a,b)|a,b e A and…

A: Here, the relation is: R=(a,b)|a,b∈A and a≡b mod 3 That is: a-b is divisible by 3. So, 7-1=6 is…

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: Let A={1,2,3,4} and let R, S, T, and U be the following relations: R={(1,1),(1,2),(1,3),(1,4)}…

A: Given :  A={1,2,3,4} and let R, S, T, and U be the following relations: R={(1,1),(1,2),(1,3),(1,4)}…

Q: Find c such that (4,−1),(−1,−8), and (c,−6) lie on a line. c=

A: We have to find the value of c such that the given three points will lie on a line.

Q: Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a…

A:

Q: (4) Let T be the partial order relation on P({1,2,..., 20}) defined by ATB if and only if |A < |B|…

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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: A partial order relation is total order relation if each of the pair of the elements are comparable.…

Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

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Q: be a filter in a space X and v be the associated net

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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),…

A:

Q: What kind of preferences are represented by a utility function of the form u(x1, x2) = x1 + √x2? Is…

A: Given Utility function of the form u(x1,x2)=x1+x2 vx1,x2=x12+2x1x2+x2 MRS (Marginal Rate of…

Q: Please solve this linear algebra question. Thank you

A: Consider the provided question, Let V be a vector space over F.

Q: For the following relation on S = {1, 2, 3, 4, 5, 6}: p = {(1, 2), (1, 6), (2, 1), (3, 5), (4, 5),…

A: According to the given information, The relation on set S = { 1,2,3,4,5,6 } is given by:

Q: 3. Suppose that {v,,v,,v,} is a linearly independent subset of R". Show that the set {v,,v, +v3,v; +…

A: The set {v1,v2,......vn} is linearly independent if for the combination, av1+bv2+......nvn=0 for…

Q: Is the set X is linearly dependent or independent X = {(1,0,1,0), (0,3,0,1), (1,1,2,2), (3,4,1, −2)}

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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: Let a = (- 4, 3, – 2) and b = (- 1, 2, – 3). Find the projection of b onto ä. proją b > V

A: Answer:Given a→=&lt;-4,3,-2&gt;b→=&lt;-1,2,-3&gt;projection b→ onto a→ is given…

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: Define the following sets e and s as follows: e = {Devin, Elsa, Floyd}, s = {Software 1, Software 2,…

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Q: Determine if the set is linearly independent. S = {(4,0,1), (0, -3,2), (5,10,0)}

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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 S = {1,2,3, 4}. For each of the following relations on S give its transitive closure. a) {(1,1),…

A: Concept: In mathematics, the transitive closure of a binary relation R on set X is the smallest…

Q: Suppose that {u, v} is a linearly independent set. Show that the set {u – v, u + v} is also linearly…

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Q: d b

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Q: Represent the following relation {1,2, 3, 4} with a matrix. {(1,1), (1, 4), (2, 2), (3, 3), (4, 1)}

A: Given below the detailed solution

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

A: The relation R will be Maiyra,Dip,Maiyra, Computer Vision,Maiyra, Pattern…

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: How many relations are there on the set {a, b}. Show all possible relations on the set {a, b} in…

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Q: Let R = {(0,1), (0,2), (1,1), (1,3), (2,2), (3,0)} Find R', the transitive closure of R

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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: Draw a directed graph (digraph) for the relation on {1,2,3,4} {(1,1), (1,4), (2,2), (3,3), (4,1)

A: From the given relation {(1,1), (1,4), (2,2), (3,3), (4,1)} on {1,2,3,4}, draw a directed graph.…

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: 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: Let F(x, y, z) = (z, x, y), ar (0,0,0), (0, 1, 1), vertices are ar

A: Introduction: Stroke's theorem is simply a higher-dimensional version of Green's theorem. The line…

Q: 2. Let X = {a,b, c, d, e, ƒ} and S be the relation on X defined by S = {(a, a), (a, b), (a, c), (a,…

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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: 3. Use the cross product properties to prove the relation (a - b) × (â+b) = 2(â × b) given a = (1,…

A: Given,a=i-3j+2kb=-2i+0j+k

Q: If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, what is the symmetric closure of R? %3D О (1, 2),…

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Q: I. Draw the directed graph and list the set of ordered pair of R, of the following. 1. If…

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Q: Let ä = (4, – 4, 0) and b = (- 1, 2, - 4). Find the projection of b onto a. proj, b = <

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