Solved: A permutation on a set can be regarded as a

Chapter 9, Problem 9.79

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A permutation on a set can be regarded as a function from thesettoitself.Forinstance,onepermutationof{1,2,3,4} is 2341. It can be identied with the function that sends each position number to the number occupying that position. Since position 1 is occupied by 2, 1 is sent to 2 or 12; since position 2 is occupied by 3, 2 is sent to 3 or 23; and so forth. The entire permutation can be written using arrows as follows: 1234 2341 a. Use arrows to write each of the six permutations of {1,2,3}. b. Use arrows to write each of the permutations of {1,2,3,4}that keep 2 and 4 xed.c. Whichpermutationsof{1,2,3}keepnoelementsxed? d. Use arrows to write all permutations of {1,2,3,4} that keep no elements xed.