If U = {x : x ∈ ℤ, −10 ≤ x ≤ 10} and A = {x : x² − 9x + 20 ≤ 0}, what is A′?
Answer and explanation
Correct answer: {−10, −9, −8, −7, −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 6, 7, 8, 9, 10}
Factor the quadratic: x² − 9x + 20 = (x − 4)(x − 5). Since the parabola opens upward, the inequality is at most zero for 4 ≤ x ≤ 5. Because the universe contains integers, A = {4, 5}. Removing these two elements from U = {−10, …, 10} gives A′ = {−10, …, 3, 6, …, 10}, listed in option A.
Frequently asked questions
What is the correct answer to this question?
{−10, −9, −8, −7, −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 6, 7, 8, 9, 10}
Why is this the correct answer?
Factor the quadratic: x² − 9x + 20 = (x − 4)(x − 5). Since the parabola opens upward, the inequality is at most zero for 4 ≤ x ≤ 5. Because the universe contains integers, A = {4, 5}. Removing these two elements from U = {−10, …, 10} gives A′ = {−10, …, 3, 6, …, 10}, listed in option A.
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.
