Exercise
The elements of A4 are
(1,2), (1,3), (1,4), (2,3), (2,4), (3,4), (1,2,3,4), (1,2,4,3),(1,3,2,4), (1,3,4,2), (1,4,2,3), (1,4,3,2).
(1), (1,2,3), (1,3,2), (1,2,4), (1,4,2), (1,3,4), (1,4,3),(2,3,4), (2,4)(2,3), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3).
(1), (1,2,3), (1,3,2), (1,2,4), (1,4,2), (1,3,4), (1,4,3),(2,3,4),(2,4,3), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3).
No, these are all the odd permutations in S4.
No, because (2,3,4) and (2,4)(2,3) define the same permutations. Then (2,4,3) is missing.
This is correct.