If A = {x ∈ R : x² − 5x + 6 ≤ 0} and B = {x ∈ R : x < 4}, what is the difference set A − B?
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Answer and explanation
Correct answer: ∅
Factor the quadratic: x² − 5x + 6 = (x − 2)(x − 3). Since the parabola opens upward, the inequality (x − 2)(x − 3) ≤ 0 holds for 2 ≤ x ≤ 3, so A = [2, 3]. Every number in [2, 3] is less than 4 and therefore belongs to B. Thus A is a subset of B, leaving no element in A − B; the answer is the empty set.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
Factor the quadratic: x² − 5x + 6 = (x − 2)(x − 3). Since the parabola opens upward, the inequality (x − 2)(x − 3) ≤ 0 holds for 2 ≤ x ≤ 3, so A = [2, 3]. Every number in [2, 3] is less than 4 and therefore belongs to B. Thus A is a subset of B, leaving no element in A − B; the answer is the empty set.
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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