Question

In a certain class there are a total of 29 majors in mathematics, 17 majors in philosophy, and 7 students who are double-majoring in both mathematics and philosophy. Suppose that there are 573 students in the entire class.

How many are majoring in neither of these subjects?

How many students are majoring in mathematics alone?

Answer 1

Students major in mathematics only = a

Students major in philosophy only = b

Students majoring in both mathematics and philosophy = c = 7

Students majoring in maths = a+c = 29

Students majoring in philosophy = b+c = 17

Students majoring in none = n

Total students = a+b+c+n = 573

a+c=29

a = 29-7 = 22

b+c = 17

b = 17-7 = 10

a+b+c+n = 573

22+10+7+n = 573

n + 39 = 573

n = 573-39 = 534

Students majoring in neither of these subjects: n = 534

Students majoring in mathematics alone: a = 22