Determining Missing Images in an Even Permutation

[Justabeginner]

Homework Statement

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?

Homework Equations

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.

 

[Fredrik]

Homework Statement

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?

Homework Equations

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.

Looks good to me.

 

[Justabeginner]

Thank you.