A college survey was taken to determine where students study. Of 112 students surveyed, 66 studied in the library, 54 studied in the student union, and 23 studied in both the library and the student union.

Of those interviewed, how many did not study in either the library or the student union?

Question

A college survey was taken to determine where students study. Of 112 students surveyed, 66 studied in the library, 54 studied in the student union, and 23 studied in both the library and the student union.

Of those interviewed, how many did not study in either the library or the student union?

kropot72 · Answer

There are five sets of students:
1) the universal set with 112 students.
2) students who studied in the library and not the student union with 66 - 23 = 43 students.
3) students who studied in the student union and not the library with 54 - 23 = 31 students.
4) students who studied in both the library and the student union with 23 students.
5) students who did not study in either the library or the student union. 

The number who did not study in either the library or the student union is found as follows:
[The number in the universal set] - [the sum of the numbers of students given in the sets described in 2), 3) and 4) above]