Question

Calculate the number of elements belonging to the sets described below:
The results of a survey of 40 incoming students show the following results:
16 students found a roommate through the school housing department.
12 students selected a roommate from a message board.
22 students knew their roommate personally.
7 students have both roommates from the housing department and message boards.
9 students have roommates from message boards and know personally.
11 students have roommates from the housing department and know personally.
5 students have roommates from all 3 sources

Answer 1

How many students did not report having roommates?

Answer 2

Is the answer 8?

Answer 3

Anybody?