If n(U) = 16 and n(A) = n(Aᶜ), what is n(A)?
Answer and explanation
Correct answer: 8
A and Aᶜ partition the universal set U, so n(A) + n(Aᶜ) = n(U). Since the two cardinalities are equal, let each one be x. Then x + x = 16, giving 2x = 16 and x = 8. Therefore n(A) = 8, so option A is correct. A value of 16 or 0 would make the two parts unequal, while 4 would account for only 8 elements altogether.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A and Aᶜ partition the universal set U, so n(A) + n(Aᶜ) = n(U). Since the two cardinalities are equal, let each one be x. Then x + x = 16, giving 2x = 16 and x = 8. Therefore n(A) = 8, so option A is correct. A value of 16 or 0 would make the two parts unequal, while 4 would account for only 8 elements altogether.
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.
