In a class of 80 students, 46 play cricket, 38 play football, and 20 play both. How many students play neither game?
Answer and explanation
Correct answer: 16
Let C be the set of students who play cricket and F the set who play football. The number playing at least one game is found by inclusion–exclusion: |C ∪ F| = |C| + |F| − |C ∩ F| = 46 + 38 − 20 = 64. Students playing neither game form the complement of C ∪ F in the class. Thus, 80 − 64 = 16 students play neither game, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Let C be the set of students who play cricket and F the set who play football. The number playing at least one game is found by inclusion–exclusion: |C ∪ F| = |C| + |F| − |C ∩ F| = 46 + 38 − 20 = 64. Students playing neither game form the complement of C ∪ F in the class. Thus, 80 − 64 = 16 students play neither game, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
