I Am studying my teacher's notes on our practice exam, And I am stuck on this part of the question where we are trying to prove that the relation is symmetric.
- Symmetry: Let x, y ∈ Q. Suppose xRy. Then ${x = 3^{k} y}$, for some k ∈ Z. Thus, y = $3^{−k}x$, where ${−k ∈ Z}$. Hence, yRx. Therefore, R is symmetric.
I am confused on as to why she made k become -k when she switched x and y. I originally thought that k would stay the same. Can anyone help me understand why she did this?