If A = {x ∈ ℝ | x² − 5x + 6 = 0} and B = {x ∈ ℝ | x² − 7x + 12 = 0}, what is A ∩ B?
Answer and explanation
Correct answer: {3}
To find each set, solve its defining quadratic equation. For A, x² − 5x + 6 = (x − 2)(x − 3) = 0, so A = {2, 3}. For B, x² − 7x + 12 = (x − 3)(x − 4) = 0, so B = {3, 4}. The intersection contains only elements present in both sets. Since 3 is common to A and B, A ∩ B = {3}. The set {2, 3, 4} would be the union, not the intersection.
Frequently asked questions
What is the correct answer to this question?
{3}
Why is this the correct answer?
To find each set, solve its defining quadratic equation. For A, x² − 5x + 6 = (x − 2)(x − 3) = 0, so A = {2, 3}. For B, x² − 7x + 12 = (x − 3)(x − 4) = 0, so B = {3, 4}. The intersection contains only elements present in both sets. Since 3 is common to A and B, A ∩ B = {3}. The set {2, 3, 4} would be the union, not the intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
