If n(Aᶜ) = 12 and n(U) = 30 for the universal set U, what is the value of n(A)?
Answer and explanation
Correct answer: 18
In a finite universal set, A and its complement Aᶜ are disjoint and together make U. Therefore their cardinalities satisfy n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 12 = 30, so n(A) = 30 − 12 = 18. Thus option B is correct. The values 12 and 30 are the complement and universal-set sizes, not n(A), while 42 incorrectly adds the quantities.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
In a finite universal set, A and its complement Aᶜ are disjoint and together make U. Therefore their cardinalities satisfy n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 12 = 30, so n(A) = 30 − 12 = 18. Thus option B is correct. The values 12 and 30 are the complement and universal-set sizes, not n(A), while 42 incorrectly adds the quantities.
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.
