If n(U) = 70, n(A) = 38, and n(Aᶜ) = 32, which statement is correct?
Answer and explanation
Correct answer: n(A) + n(Aᶜ) = n(U)
A set and its complement are disjoint and together contain every element of the universal set. Therefore, A ∪ Aᶜ = U and n(A) + n(Aᶜ) = n(U). Substituting the given values gives 38 + 32 = 70, which confirms option A. The other statements either subtract the two regions or incorrectly claim that their cardinalities are equal.
Frequently asked questions
What is the correct answer to this question?
n(A) + n(Aᶜ) = n(U)
Why is this the correct answer?
A set and its complement are disjoint and together contain every element of the universal set. Therefore, A ∪ Aᶜ = U and n(A) + n(Aᶜ) = n(U). Substituting the given values gives 38 + 32 = 70, which confirms option A. The other statements either subtract the two regions or incorrectly claim that their cardinalities are equal.
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.
