Question #N1024
A group of 100 students were surveyed about their favorite type of music. 60 students like pop music, 50 students like rock music, and 20 students like both pop and rock music. How many students like neither pop nor rock music?
A. 10
B. 20
C. 30
D. 40
Correct Answer is: A
We can use a Venn Diagram to visualize the situation. Let P represent the set of students who like pop music and R represent the set of students who like rock music. We know that |P ∩ R| = 20, |P| = 60, and |R| = 50. Since |P ∪ R| = |P| + |R| - |P ∩ R|, we have |P ∪ R| = 60 + 50 - 20 = 90. This means that 90 students like pop music, rock music, or both. Therefore, 100 - 90 = 10 students like neither pop nor rock music.