If U = {x ∈ ℤ : −6 ≤ x ≤ 6} and A = {x ∈ U : x² = 16}, what is n(Aᶜ)?
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Answer and explanation
Correct answer: 11
The integers from −6 through 6 form the universal set U, so n(U) = 13 because there are 6 negative integers, zero, and 6 positive integers. Solving x² = 16 gives x = −4 or x = 4, both of which belong to U. Thus A = {−4,4} and n(A) = 2. Therefore, n(Aᶜ) = n(U) − n(A) = 13 − 2 = 11. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The integers from −6 through 6 form the universal set U, so n(U) = 13 because there are 6 negative integers, zero, and 6 positive integers. Solving x² = 16 gives x = −4 or x = 4, both of which belong to U. Thus A = {−4,4} and n(A) = 2. Therefore, n(Aᶜ) = n(U) − n(A) = 13 − 2 = 11. 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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