If U = {x : x ∈ Z, -10 ≤ x ≤ 10} and A = {x : x ∈ U, x² ≤ 16}, what is n(A′)?
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Answer and explanation
Correct answer: 12
The condition x² ≤ 16 is equivalent to |x| ≤ 4, or −4 ≤ x ≤ 4. Since x must be an integer, A = {−4, −3, −2, −1, 0, 1, 2, 3, 4}, so n(A) = 9. The universal set contains the 21 integers from −10 to 10 inclusive. Therefore, n(A′) = n(U) − n(A) = 21 − 9 = 12.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The condition x² ≤ 16 is equivalent to |x| ≤ 4, or −4 ≤ x ≤ 4. Since x must be an integer, A = {−4, −3, −2, −1, 0, 1, 2, 3, 4}, so n(A) = 9. The universal set contains the 21 integers from −10 to 10 inclusive. Therefore, n(A′) = n(U) − n(A) = 21 − 9 = 12.
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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