logical deduction - Who is the thief? An elementary school teacher had her purse stolen

Its not mine. I found it and didnt find it when i searched so i hope you guys enjoy.
I did edit it somewhat.

An elementary school teacher had her purse stolen. The thief had to be Sammy, Karin, Arnold, Harry, or Liza. When questioned, each child made three statements:

Sammy:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Harry did it.

Karin:
(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Liza knows who did it.

Arnold:
(7) I didn’t take the purse.
(8) I didn’t know Liza before I enrolled in this school.
(9) Harry did it.

Harry:
(10) I am not guilty.
(11) Liza did it.
(12) Sammy is lying when she says I stole the purse.

Liza:
(13) I didn’t take the teacher’s purse.

(14) Karin is guilty.
(15) Arnold can vouch for me because he has known me since I was born.

Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?

Answer

It is

Karin

Because

Since 15 and 8 contradict, we have two possibilities
If 15 is False
then 14 is True => then Karin stole the purse.
If 15 is True
then 8 is False
then 9 is True.
However, if 9 is true, then 10, 11 and 12 are False, and we can't have that => 14 is False. So:
Karin did it

The lies are 3, 4, 9, 11 and 15