If the universal set is U = ℝ and A = {x ∈ ℝ : x² − 6x + 8 > 0}, what is A′?
Answer and explanation
Correct answer: [2, 4]
Factor the quadratic as x² − 6x + 8 = (x − 2)(x − 4). Since the parabola opens upward, the expression is positive outside its roots: A = (−∞, 2) ∪ (4, ∞). The points 2 and 4 are not in A because the expression equals zero there. Consequently, the complement in ℝ includes both endpoints and the interval between them, giving A′ = [2, 4]. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
[2, 4]
Why is this the correct answer?
Factor the quadratic as x² − 6x + 8 = (x − 2)(x − 4). Since the parabola opens upward, the expression is positive outside its roots: A = (−∞, 2) ∪ (4, ∞). The points 2 and 4 are not in A because the expression equals zero there. Consequently, the complement in ℝ includes both endpoints and the interval between them, giving A′ = [2, 4]. Therefore 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.
