Question

There are 20 students in a class. 14 are computer science majors, 9 are math majors, and 4 are both. How many students from the class are neither computer science nor math majors?

		3
		1
		6
		0
		Impossible to solve the problem.

Answer 1

Let, A denote the event that, a student is from computer science majors

B denotes the event that, a student is from math majors

So, AB denotes the event that a student is from Both the departments and AB denotes that a student is from either of the department.

So, we have,

#(AB) = #(A) + #(B) - #(AB)

So, #(AB) = 14 + 9 - 4 = 19

Since, there are 20 students in the class and 19 are from any of the 2 mentioned departments.

So, 20 - 19 = 1 student is neither from computer science not math majors.

The answer is 1.

Notation : # denotes the number of elements in favor of the event