Show that a cycle of odd length is an even permutation, and a cycle of even length is an oddpermutation. Hence determine which of the following members of S10 are even, or odd:(i) (1 9 3) (2 6) (4 5 10) (78)(ii) (1 9 3 2 6 ) (4 5 10 7 8),(iii) ( 1 9 3 2 6 4 5 10 ).

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Answered: Show that a cycle of odd length is an…

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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Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd permutation. Hence determine which of the following members of S10 are even, or odd: (i) ( 1 9 3) (2 6 ) ( 4 (ii) (1 9 3 2 6) (4 (iii) ( 1 9326 4 5 5 10) (78) 5 10 7 8 ), 10).