Question

Each student at some college has a mathematics requirement M (to take at least one mathematics course) and a science requirement S (to take at least one science course). A poll of 150 sophomore students shows that: 60 completed M, 45 completed S, and 25 completed both M and S
Find the number of students who have completed
(a) At least one of the two requirements
(b) Exactly one of the two requirements
(c) Neither requirement.

Answer 1

all students = 150

M = 60

S = 45

M and S = 25

(a) At least one of the two requirements:

M or S = M + S - (M and S) = 60 + 45 - 25 = 80

(b) Exactly one of the two requirements:

(M or S) - (M and S) = 80 - 25 = 55

(c) Neither requirement:

(all students) - (M or S) = 150 - 80 = 70