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5. Consider the permutations 1234 2 1 3 4 on the set {1, 2, 3, 4). Find fog and go f. (a) (b) F Find f, and verify that ƒoƒ-¹ (c) () Find g¹, and verify that 1 gog-¹- - and g = 1 2 3 4 3142 1 2 3 4 1234 1 2 3 4 1234 1) = 5¹ of =g-log

5. Consider the permutations 1234 2 1 3 4 on the set {1, 2, 3, 4). Find fog and go f. (a) (b) F Find f, and verify that ƒoƒ-¹ (c) () Find g¹, and verify that 1 gog-¹- - and g = 1 2 3 4 3142 1 2 3 4 1234 1 2 3 4 1234 1) = 5¹ of =g-log

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 56E: Let f1,f2,...,fn be permutations on a nonempty set A. Prove that (f1f2...fn)1=fn1=fn1...f21f11 for...
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5. Consider the permutations f on the set {1, 2, 3, 4). Find (a) (b) (c) ( 1 2 3 4 2134 fog and go f. Find f-1, and verify that ƒoƒ-¹ = Find g, and verify that gog-¹ = - 1 2 3 4) = 5¹ of =g-log and g = 1 2 3 4 1 234 (1234) - 3 4 1 4 2
Transcribed Image Text:5. Consider the permutations f on the set {1, 2, 3, 4). Find (a) (b) (c) ( 1 2 3 4 2134 fog and go f. Find f-1, and verify that ƒoƒ-¹ = Find g, and verify that gog-¹ = - 1 2 3 4) = 5¹ of =g-log and g = 1 2 3 4 1 234 (1234) - 3 4 1 4 2
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