3. Let S represent the students who study
statistics, C represent the students who study calculus, and L represent the students who
study logic.
We must find n(S Ç C Ç
L). We know that
n(S È C È L) = n(S) + n(C) + n(L) - n(S Ç C) - n(S Ç L) - n(C Ç L) + n(S Ç C Ç L).
Hence,
2092 = 1232 + 879 + 114 - 103 - 23 - 14 + n(S Ç C Ç L).
Thus n(S Ç C Ç L)=7, that is, 7 students have taken all three courses.