Thread: Noob Help, Three way set intersection.

Hi this is my first post and thanks in advance.

Im trying to do a three way intersection here is my question.

1. Suppose that 25 people attended a conference with three sessions, where 15 people attended the first session, 18 the second session, and 12 the third session. At least how many people attended all three sessions?

So far I have:
First u Second = First + Second - |First n Second|
First n Second >= 15 + 12 - 25
First n Second >= 8

25>= (First n Second) u Third = (First n Second) + Third - |First n Second n Third|

and when I do all of this i get First n Second n Third >= -5 !!

Ive been reading everything to figure this out.

BTW Im pretty sure the answer is 0. IE
15 ppl attend first.
The other 10 attend Second plus 8 From the original 15.
Then all 10 of the second attend and 2 of the original 15 that havnt gone to two attend. So maybe my -5 if correct. So 5 ppl may not of attended any?