Needed to be solved correctly in the order to get positive feedbackPlease provide me hundred percent correct solutionBy hand and neat and clean solution needed for it 27.4.3 Let X = {1,2,3}. Define the relation R = {(1, 1), (1,2), (1,3), (2, 1), (2, 2), (3, 1), (3,3)} on X.(a) Which of the properties reflexive, symmetric, transitive are satisfied by R?(b) Compute the sets A1, A2, A3 where A₁ = {xEX: xRn}. Show that {A1, A2, A3} do notform a partition of X.(c) Repeat parts (a) and (b) for the relations S and T on X, whereS = {(1, 1), (1,3), (3, 1), (3,3)}T = {(1, 1), (1,2), (1,3), (2, 1), (2, 2), (2,3), (3,3)}Some of the sets A1, A2, A3 might be the same in each of your examples. If, for example, A1 = A3, thenthe collection {A₁, A2, A3} only contains two sets: {A₁, A2}. Is this a partition? Compare with theexample on page 149

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7.4.3 Let X = {1,2,3}. Define the relation R = {(1, 1), (1,2), (1,3), (2, 1), (2, 2), (3, 1), (3,3)} on X. (a) Which of the properties reflexive, symmetric, transitive are satisfied by R? (b) Compute the sets A₁, A2, A3 where A₁ = {x € X: x Rn}. Show that {A1, A2, A3} do not form a partition of X. (c) Repeat parts (a) and (b) for the relations S and T on X, where S = {(1,1), (1,3), (3,1), (3,3)} T = {(1, 1), (1,2), (1,3), (2, 1), (2, 2), (2,3), (3,3)} Some of the sets A1, A2, A3 might be the same in each of your examples. If, for example, A1 = A3, then the collection {A₁, A2, A3} only contains two sets: {A₁, A2}. Is this a partition? Compare with the example on page 149

7.4.3 Let X = {1,2,3}. Define the relation R = {(1, 1), (1,2), (1,3), (2, 1), (2, 2), (3, 1), (3,3)} on X. (a) Which of the properties reflexive, symmetric, transitive are satisfied by R? (b) Compute the sets A₁, A2, A3 where A₁ = {x € X: x Rn}. Show that {A1, A2, A3} do not form a partition of X. (c) Repeat parts (a) and (b) for the relations S and T on X, where S = {(1,1), (1,3), (3,1), (3,3)} T = {(1, 1), (1,2), (1,3), (2, 1), (2, 2), (2,3), (3,3)} Some of the sets A1, A2, A3 might be the same in each of your examples. If, for example, A1 = A3, then the collection {A₁, A2, A3} only contains two sets: {A₁, A2}. Is this a partition? Compare with the example on page 149

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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