Let S, denote the symmetric group on n letters and let p and q be prime numbers. (a) What is the smallest n such that S, has an element of order p? (b) What is the smallest n such that S, has an element of order p? (c) What is the smallest n such that S, has an element of order pq? 112 (d) EXTRA CREDIT: Suppose m is a composite number and let m = ppp be its prime decomposition. Find the smallest n such that S, has an element of order m.