If U = {x : x ∈ ℤ, −12 ≤ x ≤ 12} and A = {x : x ∈ U, x² − 9x + 18 ≤ 0}, what is n(A′)?
Answer and explanation
Correct answer: 21
Factor the quadratic inequality: x² − 9x + 18 = (x − 3)(x − 6). Since the parabola opens upward, the inequality is non-positive for 3 ≤ x ≤ 6. The integer elements of A are therefore 3, 4, 5, and 6, so n(A) = 4. The universal set contains all integers from −12 through 12, giving 25 elements. Hence n(A′) = 25 − 4 = 21, so option D is correct.
Frequently asked questions
What is the correct answer to this question?
21
Why is this the correct answer?
Factor the quadratic inequality: x² − 9x + 18 = (x − 3)(x − 6). Since the parabola opens upward, the inequality is non-positive for 3 ≤ x ≤ 6. The integer elements of A are therefore 3, 4, 5, and 6, so n(A) = 4. The universal set contains all integers from −12 through 12, giving 25 elements. Hence n(A′) = 25 − 4 = 21, so option D 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.
