If n(U) = 30 and n(Aᶜ) = 18, what is n(A)?
Answer and explanation
Correct answer: 12
A and its complement Aᶜ are disjoint and together contain every element of U. Therefore, n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 18 = 30, so n(A) = 30 − 18 = 12. Thus option A is correct. Option C is the size of the complement, option D is the size of U, and option B is impossible because a subset cannot have more elements than its universal set.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
A and its complement Aᶜ are disjoint and together contain every element of U. Therefore, n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 18 = 30, so n(A) = 30 − 18 = 12. Thus option A is correct. Option C is the size of the complement, option D is the size of U, and option B is impossible because a subset cannot have more elements than its universal set.
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.
