If A = {x ∈ R : 0 ≤ x ≤ 4} and B = {x ∈ R : x² − 4x + 3 ≤ 0}, what is A ∩ B?
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Answer and explanation
Correct answer: [1, 3]
Factor the quadratic: x² − 4x + 3 = (x − 1)(x − 3). Since the parabola opens upward, the inequality (x − 1)(x − 3) ≤ 0 holds for 1 ≤ x ≤ 3. Thus B = [1, 3]. This interval is already contained in A = [0, 4], so their intersection is [1, 3]. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
[1, 3]
Why is this the correct answer?
Factor the quadratic: x² − 4x + 3 = (x − 1)(x − 3). Since the parabola opens upward, the inequality (x − 1)(x − 3) ≤ 0 holds for 1 ≤ x ≤ 3. Thus B = [1, 3]. This interval is already contained in A = [0, 4], so their intersection is [1, 3]. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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