In a class of 50 students, 30 like Math, 25 like Science, and 10 like both. How many students like neither Math nor Science?
Answer: A
Let M be the set of students who like Math and S be the set of students who like Science.
n(M) = 30, n(S) = 25, n(M ∩ S) = 10.
Number of students who like at least one subject is n(M ∪ S) = n(M) + n(S) - n(M ∩ S) = 30 + 25 - 10 = 45.
Total students = 50.
Number of students who like neither = Total students - n(M ∪ S) = 50 - 45 = 5.