1. Consider the permutation function p, on the set A = {1, 2. 4, 8, 16, 32, 64}. In all cases except 64: PI (x) = 2x 64 is specifically mapped to 1. In other words, p, (64) = 1. Write this function in standard permutation notation. 2. Consider the permutation function p2 on a set A defined by: (abcdefghy (gheachdf) a. Find A b. Represent p2 as a set of ordered pairs. 3. pa is a permutation on the set A = {w, x, y, z} as defined by: 10 0 0] Mp3 = 0001 0100 10010 a. Represent pa in standard permutation notation b. Represent py by finding its digraph4. Given the following permutations, answer the questions below. abcdefghij (abcdefgnil) and P=lebgeifhiad PA=( dhebifagcj a. Find PF1 b. Find P5P4 C. Find (P5 P4) -1 d. Write Ps as a product of cycles e. Write PA as a product of transpositions f. Is PA even or odd? g. If Pa is a permutation on the set fa, b, c, d, e, f, gh, i, ]} represented by the cycle below, write P: in full permutation notation: P& = (c. e. g. La. f )