Assignment:
Q1. Prove that the subgroup of A4 generated by any element of order 2 and and any element of order 3 is all of A4.
Q2. Prove that if x and y are distinct 3-cycles in S4 with x != y^-1 (x not equal to the inverse of y), then the subgroup of S4 generated by x and y is all of A4.
Provide complete and step by step solution for the question and show calculations and use formulas.