If A = {x : x ∈ ℕ, x² − 7x + 12 = 0} and B = {3, 4}, which statement is correct?
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Answer and explanation
Correct answer: A = B
Factor the quadratic equation: x² − 7x + 12 = (x − 3)(x − 4) = 0. Therefore, the natural-number solutions are x = 3 and x = 4, so A = {3, 4}. Since B is also exactly {3, 4}, the two sets have the same elements and hence A = B. The order of elements does not matter in a set.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Factor the quadratic equation: x² − 7x + 12 = (x − 3)(x − 4) = 0. Therefore, the natural-number solutions are x = 3 and x = 4, so A = {3, 4}. Since B is also exactly {3, 4}, the two sets have the same elements and hence A = B. The order of elements does not matter in a set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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