If A = {x : x² − 7x + 12 = 0} and B = {x : x² − 9x + 20 = 0}, what is A ∪ B?
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Answer and explanation
Correct answer: {3, 4, 5}
Factor the first equation: x² − 7x + 12 = (x − 3)(x − 4) = 0, so A = {3, 4}. Factor the second equation: x² − 9x + 20 = (x − 4)(x − 5) = 0, so B = {4, 5}. The union contains every distinct element appearing in either set, so A ∪ B = {3, 4, 5}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{3, 4, 5}
Why is this the correct answer?
Factor the first equation: x² − 7x + 12 = (x − 3)(x − 4) = 0, so A = {3, 4}. Factor the second equation: x² − 9x + 20 = (x − 4)(x − 5) = 0, so B = {4, 5}. The union contains every distinct element appearing in either set, so A ∪ B = {3, 4, 5}. 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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