If n(Aᶜ) = 58 and n(U) = 132, what is n(A)?
Answer and explanation
Correct answer: 74
A set and its complement divide the universal set into two non-overlapping parts. Hence n(A) + n(Aᶜ) = n(U). Substituting the given values, n(A) + 58 = 132, so n(A) = 132 − 58 = 74. Therefore, option B is correct. The complement is not subtracted from A; together, A and Aᶜ account for every element of U exactly once.
Frequently asked questions
What is the correct answer to this question?
74
Why is this the correct answer?
A set and its complement divide the universal set into two non-overlapping parts. Hence n(A) + n(Aᶜ) = n(U). Substituting the given values, n(A) + 58 = 132, so n(A) = 132 − 58 = 74. Therefore, option B is correct. The complement is not subtracted from A; together, A and Aᶜ account for every element of U exactly once.
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.
