A class has 90 students, so the universal set U has n(U) = 90. If A is the set of students who like science and n(Aᶜ) = 34, how many students like science?
Answer and explanation
Correct answer: 56
The complement Aᶜ contains all students in the universal set who do not belong to A. Since A and Aᶜ are disjoint and together make U, their cardinalities satisfy n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 34 = 90, so n(A) = 90 − 34 = 56. Therefore, 56 students like science, making option A correct.
Frequently asked questions
What is the correct answer to this question?
56
Why is this the correct answer?
The complement Aᶜ contains all students in the universal set who do not belong to A. Since A and Aᶜ are disjoint and together make U, their cardinalities satisfy n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 34 = 90, so n(A) = 90 − 34 = 56. Therefore, 56 students like science, making option A 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.
