c. Complete the following statements:The group S8Sym (Ns) of all permutations on the set Ng{1, 2, 3, 4, 5, 6, 7, 8} is ?group since fg ?gf.The group S8Sym (N3) of all permutations on the set Ng{1, 2, 3, 4, 5, 6, 7, 8} is ?group since the order of the group S8 is|S8|Note: Note that the notation fg means fo g, where o is the function composition. Be aware of the order of the operation. For instance, if f (x)2x andg (x) = sin z, then (f o g) (x) = f (9 (x)) = f (sin a) = (sin z)", which is not equal to sin (z?) = (go f) (x).

Answered: Image /qna-images/answer/02cc4063-9fc9-4385-ad7c-797d6fc1c05f.jpg

c. Complete the following statements: The group Sg = Sym (Ng) of all permutations on the set Ng {1,2, 3, 4, 5, 6, 7, 8} is ? v group since fg ? gf. The group Sg = Sym (N3) of all permutations on the set Ng = {1,2, 3, 4, 5,6, 7, 8} is ? v group since the order of the group S3 is |S8 Note: Note that the notation fg means fo g, where o is the function composition. Be aware of the order of the operation. For instance, if f (x) = 2x and G (x) = Sin z, then (f o g) (a) = f (g ()) = f (sin z) = (sin æ)", which is not equal to sin (x?) = (go f) (x).

c. Complete the following statements: The group Sg = Sym (Ng) of all permutations on the set Ng {1,2, 3, 4, 5, 6, 7, 8} is ? v group since fg ? gf. The group Sg = Sym (N3) of all permutations on the set Ng = {1,2, 3, 4, 5,6, 7, 8} is ? v group since the order of the group S3 is |S8 Note: Note that the notation fg means fo g, where o is the function composition. Be aware of the order of the operation. For instance, if f (x) = 2x and G (x) = Sin z, then (f o g) (a) = f (g ()) = f (sin z) = (sin æ)", which is not equal to sin (x?) = (go f) (x).

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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