If U = R and A = {x ∈ R : x² + 2x − 8 < 0}, what is A′?
Answer and explanation
Correct answer: (−∞, −4] ∪ [2, ∞)
Factor the quadratic: x² + 2x − 8 = (x + 4)(x − 2). Since the parabola opens upward, the inequality (x + 4)(x − 2) < 0 holds strictly between the roots, so A = (−4, 2). Because the universal set is R, the complement contains all real numbers outside this open interval, including the endpoints −4 and 2. Hence A′ = (−∞, −4] ∪ [2, ∞).
Frequently asked questions
What is the correct answer to this question?
(−∞, −4] ∪ [2, ∞)
Why is this the correct answer?
Factor the quadratic: x² + 2x − 8 = (x + 4)(x − 2). Since the parabola opens upward, the inequality (x + 4)(x − 2) < 0 holds strictly between the roots, so A = (−4, 2). Because the universal set is R, the complement contains all real numbers outside this open interval, including the endpoints −4 and 2. Hence A′ = (−∞, −4] ∪ [2, ∞).
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.
