If the universal set U has n(U) = 72 and n(Aᶜ) = 31, what is the value of n(A)?
Answer and explanation
Correct answer: 41
A and its complement Aᶜ are disjoint, and together they make the universal set U. Therefore their cardinalities satisfy n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 31 = 72, so n(A) = 72 − 31 = 41. Thus option A is correct. The other values represent either a sum or one of the given cardinalities.
Frequently asked questions
What is the correct answer to this question?
41
Why is this the correct answer?
A and its complement Aᶜ are disjoint, and together they make the universal set U. Therefore their cardinalities satisfy n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 31 = 72, so n(A) = 72 − 31 = 41. Thus option A is correct. The other values represent either a sum or one of the given cardinalities.
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.
