Determine whether each of the following is a closed set.(a) A = [2,3] U [4,7](b) B = (-∞, 2] U [3,5](c) C = R \(-1,1)(d) D= [1,2) U [2, 4](e) E = (1, 2) U (3, 4]

As per bartleby guidelines we do only first three subparts and rest part can be reposted separately.

Answered: Determine whether each of the following…

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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Which of the following operations on the set Z has more than one left neutral element and no right neutral element? (a) a ° b = b - a (b) a°b = b (c) a°b = a + ab - 1 (d) a°b = ab (e) Such a prescription does not exist.
6. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation xRy when x + y is divisible by 3, then R = O {1, 2), (2, 4)} all of these O {(1, 2), (2, 4), (3, 3)} O {1, 2), (3, 3)}
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Define relations R 1 , … , R 6 on { 1 , 2 , 3 , 4 } by R 1 = { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) } , R 2 = { ( 1 , 1 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 3 = { ( 2 , 4 ) , ( 4 , 2 ) } , R 4 = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) } , R 5 = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 6 = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 1 ) , ( 3 , 4 ) } , Which of the following statements are correct? Check ALL correct answers below. A. R 2 is not transitive B. R 4 is antisymmetric C. R 5 is transitive D. R 6 is symmetric E. R 3 is transitive F. R 3 is reflexive G. R 3 is symmetric H. R 2 is reflexive I. R 4 is transitive J. R 5 is not reflexive K. R 4 is symmetric L. R 1 is not symmetric M. R 1 is reflexive
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Determine whether each of the following is a closed set. (a) A = [2,3] U [4,7] (b) B = (-∞, 2] U [3,5] (c) C = R \(-1,1) (d) D= [1,2) U [2, 4] (e) E = (1, 2) U (3, 4]