# 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
```