# Exercise 12.3.4

Is the operation of deletion "commutative" in the sense that deleting $x$ and then $y$ from a binary search tree leaves the same tree as deleting $y$ and then $x$? Argue why it is or give a counter example.

It's not commutative. Let's explore the following tree:

     2
/   \
1       4
/
3


If we first delete 1, and then 2 we get:

     2              4
\          /
4      3
/
3


If we do it the other way around, deleting 2 first, we replace it with its successor (3) and then when we delete 1, we get:

     3          3
/   \          \
1       4          4