If U = {x ∈ ℕ | 1 ≤ x ≤ 20} and A = {x ∈ U | x is a prime number}, how many elements does Aᶜ contain?
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Answer and explanation
Correct answer: 12
The universal set contains the 20 natural numbers from 1 through 20. The primes in this range are 2, 3, 5, 7, 11, 13, 17, and 19, so n(A) = 8. Since the complement contains all non-prime members of U, n(Aᶜ) = n(U) - n(A) = 20 - 8 = 12. Number 1 is not prime and is correctly included in the complement.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The universal set contains the 20 natural numbers from 1 through 20. The primes in this range are 2, 3, 5, 7, 11, 13, 17, and 19, so n(A) = 8. Since the complement contains all non-prime members of U, n(Aᶜ) = n(U) - n(A) = 20 - 8 = 12. Number 1 is not prime and is correctly included in the complement.
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.
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