If U = {x : x is a digit} and A = {x : x is a prime digit}, what is n(Aᶜ)?
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Answer and explanation
Correct answer: 6
The digits in the universal set are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, so n(U) = 10. The prime digits are 2, 3, 5, and 7, giving n(A) = 4. The complement Aᶜ contains all digits in U that are not prime: {0, 1, 4, 6, 8, 9}. Therefore, n(Aᶜ) = n(U) − n(A) = 10 − 4 = 6. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The digits in the universal set are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, so n(U) = 10. The prime digits are 2, 3, 5, and 7, giving n(A) = 4. The complement Aᶜ contains all digits in U that are not prime: {0, 1, 4, 6, 8, 9}. Therefore, n(Aᶜ) = n(U) − n(A) = 10 − 4 = 6. Hence, option A is correct.
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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