Determine the transitive closure of the relation R~  given by the following matrix: R~ =  0.3 0.9 0.5 0.5 1 0.7 1 0.7 0.4

Q: Q2. Let X = {a, b, c, d, m, n}, 7 = {6, X, {c}. {m,n}, {a, b, c, d}, {c, m, n}}. and Y- (b,c, m) C…

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Q: Which of the following sets is linearly independent? * O M={ (3,6 ).(6,12),(1,2)} O M={…

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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: Let A= {1, 2, 3, 4} and let the relation R on A be defined by the matrix [1110 0101 MR then which of…

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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…

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Q: Consider the relation described by the following digraph: Write the matrix of this relation. Use the…

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Q: Let A = {0,1,2} and r = {(0,0), (1,1), (2,2 y that r is an equivalence relation on A.

A: The relation is reflexive, since a,a∈R, where a∈A Also, since a=b where (a,b)∈R therefore, the…

Q: Let A = {1, 2, 3, 4}. Define a relation R on A: R = {(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4, 3)}…

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Q: (a) Let V be as defined below. 221 -13 -8 4 V = 6 -13 5 -9 {v1,v2,v3,v4}={ { 14, -8, -4, -4, 4}, {…

A: No. V is not linearly independent set because we can see that the number of rows in V are 4 and the…

Q: Suppose that S = {v} is a linearly dependent set. What is v?

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Q: = {(: ") e v : a,b,c, € F}, w. = { (; ") : a, 6.c € F}- a b { (; 2) : a,6, c € F}. Find the basis…

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Q: "Consider the relations R₁, R₂, R3 R4 R5 on A = {1, 2, 3, 4} defined by R₁ = {(1, 2), (2, 1)} R₂=…

A: A relation R on the set A={1,2,3,4} is reflexive if (1,1),(2,2),(3,3),(4,4) are all elements of R.…

Q: 5. Let R be a relation on R2 defined by (w1,y1)R(x2y2) if and only if yı +x1 = y2 + x2. (a) Is R…

A: Given relation is

Q: (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…

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Q: Does the set S = {(1,2, 3), (0, 1, 2), (-2,0, 1)}span R³? %3D O Yes O No

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Q: Exercise 12.1 Which of the following subsets of R? are (a) path-connected (b) connected? Connected…

A: We shall solve first three subparts only - for others kindly post again by mentioning properly.

Q: 19. Let R= 1010 1100 0011 0100 be the adjacency matrix for a relation r on the set A = {1,2,3,4}.…

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Q: Α) Reflexive (No), symmetric (No), transistive (No) Reflexive (Yes), symmetric (Yes), transistive…

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Q: Determine if the set of functions {e* , xe* , x²e* }is linearly independent or linearly dependent. O…

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Q: 0 0 8008 a 10 10 b 0 1 0 1 C d 0 1 0 1 10 10 Reflexive Irreflexive Symmetric Antisymmetric…

A: The given matrix for the relation  is:Determine the relation.Definition: Let  be relation on the set…

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A: To given subspaces are W1=x1,x2,x3:x1+x2+x3=0W2=Lin1,1,1 To prove ℝ3=W1⊕W2 In order to prove that…

Q: Definition: If A, B = Matnxn (C), we say A and B are conjugate if there is an invertible matrix C…

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Q: Let A = {3, 5, 6} ,R relation on A defined by R = {(a, b) : a < b, a, b e A}. rit O a. {(5,3),…

A: If A= {3, 5,6} , Where R = {(a, b) : a&lt;b, a, b€A) } Find R?

Q: Let A = {1, 2, 3, 4} and R be a relation defined on A. Given that R= {(1, 1), (1, 3), (2, 2), (2,…

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Q: Given X = {1,3,5}. R is a relation on X, defined by aR,b if and only if la – bl is an even integer.…

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Q: Let R be the relation on S={1,2,3} given by R={(1,1).(1,2).(2.1).(2.2),(3,1).(3.2)}. Then the…

A: Answer is mentioned below