. 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: 10) (78) (i) (19 3) ( 6) (45 (ii) (1 9 3 2 6 ) (4 5 10 7 8), (iii) (1 9 3 2 6 4 5 10).

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6. 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) (19 3) (2 6) (4 5 10 ) (78)
1 9 3 2 6) (4 5 10 7 8),
(iii) 1 9 3 2 6 4 5 10).
Transcribed Image Text:6. 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) (19 3) (2 6) (4 5 10 ) (78) 1 9 3 2 6) (4 5 10 7 8), (iii) 1 9 3 2 6 4 5 10).
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