A permutation on a set can be regarded as a function from

Chapter 9, Problem 47E

(choose chapter or problem)

A permutation on a set can be regarded as a function from the set to itself. For instance, one permutation of {1, 2, 3, 4} is 2341. It can be identified 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 1 ? 2; since position 2 is occupied by 3, 2 is sent to 3 or 2 ? 3; and so forth. The entire permutation can be written using arrows as follows: 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 fixed.________________c. Which permutations of {1, 2, 3} keep no elements fixed?________________d. Use arrows to write all permutations of {1, 2, 3, 4} that keep no elements fixed.