If n(U) = 64 and n(A′) = 19, what is n(A)?
Answer and explanation
Correct answer: 45
A set and its complement partition the universal set into two disjoint parts. Consequently, their cardinalities satisfy n(A) + n(A′) = n(U). Substituting the given values gives n(A) + 19 = 64, so n(A) = 64 − 19 = 45. Option C gives the size of the complement, while option B incorrectly adds the two numbers. Option D would be possible only if A′ were empty.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
A set and its complement partition the universal set into two disjoint parts. Consequently, their cardinalities satisfy n(A) + n(A′) = n(U). Substituting the given values gives n(A) + 19 = 64, so n(A) = 64 − 19 = 45. Option C gives the size of the complement, while option B incorrectly adds the two numbers. Option D would be possible only if A′ were empty.
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.
