If U = {x : x ∈ ℕ, x ≤ 40}, A = {x ∈ U : x is even}, and B = {x ∈ U : x is a square number}, what is n(A′ ∩ B′)?
Answer and explanation
Correct answer: 17
A′ ∩ B′ consists of elements that are neither even nor square. Thus they must be odd, non-square natural numbers not exceeding 40. There are 20 odd numbers from 1 through 40. The odd square numbers in this range are 1, 9, and 25; these must be excluded. Therefore n(A′ ∩ B′) = 20 − 3 = 17, so option A is correct. The square 49 is outside U and is not considered.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
A′ ∩ B′ consists of elements that are neither even nor square. Thus they must be odd, non-square natural numbers not exceeding 40. There are 20 odd numbers from 1 through 40. The odd square numbers in this range are 1, 9, and 25; these must be excluded. Therefore n(A′ ∩ B′) = 20 − 3 = 17, so option A is correct. The square 49 is outside U and is not considered.
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.
