3. Exercise $2.2.4 Let H C S4 be the subset consisting of: all 3-cycles, all products of disjoint 2-cycles, and the identity. a. Show that U := {e, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)} is a subgroup of S4. b. Show that the product of any two 3 -cycles in S4 is either: the identity, a 3-cycle, or a product of two disjoint 2-cycles (see book for hints). c. Show that the product of a 3-cycle in S4 with any product of two disjoint 2-cycles is a 3-cycle. d. Show that H is a subgroup of S4