In a class of 120 students, 72 are in the mathematics set M, 64 are in the physics set P, and 28 are in both sets. How many students are in neither M nor P?
Answer and explanation
Correct answer: 12
To find the number of students in at least one of the two sets, use the inclusion-exclusion formula: |M ∪ P| = |M| + |P| − |M ∩ P|. Thus |M ∪ P| = 72 + 64 − 28 = 108. The remaining students belong to neither set, so subtract the union from the total: 120 − 108 = 12. Therefore, 12 students are in neither mathematics nor physics.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
To find the number of students in at least one of the two sets, use the inclusion-exclusion formula: |M ∪ P| = |M| + |P| − |M ∩ P|. Thus |M ∪ P| = 72 + 64 − 28 = 108. The remaining students belong to neither set, so subtract the union from the total: 120 − 108 = 12. Therefore, 12 students are in neither mathematics nor physics.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
