Permutation - Missing Images

1. The problem statement, all variables and given/known data

Hi, I have been MIA lately due to work, but I am back with questions, and eager to learn! I am self studying, and so I have inconsistencies in my learning which I hope to iron out.



Suppose you are told that the permutation

( 1 2 3 4 5 6 7 8 9

3 1 2 X Y 7 8 9 6)



In S9 the symmetric group, where the images of 5 and 4 have been lost, is an even permutation. What must the images of 5 and 4 be?





2. Relevant equations







3. The attempt at a solution

I thought X should be 5, and Y should be 4, so that you have 6 transpositions or am I oversimplifying the logic here?

Thank you.