7. Represent the relation R on {1, 2, 3, 4} with a matrix (with the elements of this set listed in order). R ={(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4,3)}

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

A:

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

A: Given A = {1, 2, 3, 4}. The relation R = {(1, 2), (2, 1), (2, 3), (3, 4), (4, 1)} Find the matrix…

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: If R is a relation defined from the Set A ={ 6,12,25,36} to the set B = {3,4,5,6} as follows: {(x,…

A: Part (i):   Relation set of R in the roster form:

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 A = {1, 2, 3, 4, 5}. Define the following relations on A. R1 = {(1,1), (1,2), (2,1), (3,2),…

A:

Q: Given the following relation, { ( A, A ), ( A, B ), ( A, E ), ( B, B ), ( B, E ), ( C, A ), ( C, B…

A: Given the following relation, {(A, A), (A, B), (A, E), (B, B), (B, E), (C, A), (C, B), (C, C), (C,…

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: 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: O List the ordered pairs in the relations on (1,2,3,4) Gi) Draw the direted graph representing the…

A: Given the matrix of relation R A=1101101001111011

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

A: A set  is said to be well-ordered if it has a total order and has the property that every non-empty…

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: Consider two fuzzy relations [! 0.1 0.3] R=0.8 0.6 0.9 and S=0.2 0.4 0.9 0 03 0.2 0.5 0.7 0,2 0.7…

A: Let R1 and R2 be two fuzzy relations. The max-min composition of R1 and R2 is defined as follows.…

Q: Show whether the set {(2, –1, 3), (0, 3, 1), (- 1,1, -2)} in the space R³ is linearly independent.

A: Definition. Let V be a vector space. Vectors v1, v2, . . . ,vk ∈ V are  called linearly dependent if…

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

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Q: Exercise 5.2.1: Here are two relations: R(A, B): {(0,1), (2,3), (0,1), (2,4), (3,4)} S(B,C): {(0,1),…

A: Given: a. Compute πA+B, A2, B2R A B A+B A2 B2 0 1 1 0 1 2 3 5 4 9 0 1 1 0 1 2 4 6 4 16…

Q: Suppose that N+ 1 balls, of which a+b+1 are red and N-a-bare blue, are arranged in a linear order in…

A: From the given information, There are N+1 balls, of which a+b+1 are red and N-a-b are blue arranged…

Q: A. Let R be a relation on set A. A={x: xeJ and 0 sxs 12), and R-{(a,b) : la - b| is multiple of 6}.…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: If R is a relation defined from the Set A = { 6,12,25,36} to the set B = {3,4,5,6} as follows: R =…

A: Since you have asked multiple sub-parts, we are answering the first three sub-parts for you now. If…

Q: Please solve this linear algebra question. Thank you

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

Q: Let S = {0, 1, 2, 3} and the relations A, B, and C on S are as follows: А %3 (0, 0), (0, 1), (0, 3),…

A: Equivalence Relation An equivalence relation on a set S is a subset of SXS, i.e., a collection  of…

Q: 1. Let A = {2, 3, 4, 5, 6, 7, 8) and R a relation over A. Draw the directed graph and the binary…

A: The solution is given by using the definition of matrix representation and directed graph of the…

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: 5- Consider the following arrays VERT={1,2,6,4} , TAIL={1,2,2,4,4,3,4,1} , HEAD={2,2,3,3,4,4,1,3},…

A: Given the sets Tail=1,2,2,4,4,3,4,1 and Head=2,2,3,3,4,4,1,3, the digraph can be computed using the…

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…

A:

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

A:

Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

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: Which functions on {1, 2, 3, 4} x {a, b, c} is NOT onto? О {1, с). (2, а). (3, b). (4, b)} О {(1,…

A: Given sets are {1,2,3,4} and {a,b,c}. We know that a function f from A to B is called onto if for…

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: Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows: %3D R = {(0, 1), (1,1), (2,…

A:

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8}.  How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

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: 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: 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: Let S = (0, 1, 2, 3} and the relations A, B, and C on S are as follows: %3D A = {(0, 0), (0, 1), (0,…

A:

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…

A:

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

A:

Q: Let R1 = {(1,1), (1, 2)} and R2 = {(1,1), (2, 2)} be relations on A = {1,2}. Then R1 U R2 = .... O…

A: Let ,  R1 = {(1, 1), (1, 2)} and R2 = {(1, 1), (2, 2)} be relations on A = {1, 2}  We have to find…

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: 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),…

A:

Q: Let A = {2, 4} and B = {1, 3, 5} and define rela- tions U, V, and W from A to B as follows: For…

A: (a) First obtain the 3 relations as follows.

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: 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…

A: