Question

In a group of 50 students, 30 like mathematics, 25 like science, and 15 like both. How many students do not like either mathematics or science?

• A. 10
• B. 15
• C. 20
• D. 5

Hint:

Use the principle of inclusion and exclusion to find the number of students who like at least one of the subjects, and then subtract from the total to find those who like neither.

Answer 1

The Correct Option is D

Step 1: Use the principle of inclusion and exclusion. Let:
\( M \) be the set of students who like mathematics,
\( S \) be the set of students who like science,
\( |M \cup S| \) be the number of students who like mathematics or science.
We are given:
\( |M| = 30 \) (students who like mathematics),
\( |S| = 25 \) (students who like science),
\( |M \cap S| = 15 \) (students who like both mathematics and science).
The number of students who like either mathematics or science is given by the principle of inclusion and exclusion: \[ |M \cup S| = |M| + |S| - |M \cap S| = 30 + 25 - 15 = 40. \] Step 2: Calculate the number of students who do not like either. The total number of students is 50, so the number of students who do not like either subject is: \[ 50 - |M \cup S| = 50 - 40 = 5. \] Thus, the correct answer is: \[ \boxed{5}. \]