If A = {x : x² − 5x + 6 = 0} and B = {2, 3}, which statement is correct?
Answer and explanation
Correct answer: A = B
Factor the equation as x² − 5x + 6 = (x − 2)(x − 3) = 0. Thus x = 2 or x = 3, so A = {2,3}. This is exactly the same set as B, which means A = B. The value 6 is the constant term, not a solution, and the equation is not without solutions. Therefore, options B, C, and D are false, and option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Factor the equation as x² − 5x + 6 = (x − 2)(x − 3) = 0. Thus x = 2 or x = 3, so A = {2,3}. This is exactly the same set as B, which means A = B. The value 6 is the constant term, not a solution, and the equation is not without solutions. Therefore, options B, C, and D are false, and option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
