If A = {x : x is a solution of x² - 5x + 6 = 0} and B = {2, 3}, which statement is true?
Answer and explanation
Correct answer: A = B
Factor the quadratic equation: x² - 5x + 6 = (x - 2)(x - 3). Therefore its solutions are x = 2 and x = 3, so the solution set is A = {2, 3}. Since B is also {2, 3}, the two sets have exactly the same elements and A = B. Option B confuses the constant term with the solution set. Option C is false because a proper subset must be smaller than the other set, while these sets are equal. Option D is false because their intersection is {2, 3}.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Factor the quadratic equation: x² - 5x + 6 = (x - 2)(x - 3). Therefore its solutions are x = 2 and x = 3, so the solution set is A = {2, 3}. Since B is also {2, 3}, the two sets have exactly the same elements and A = B. Option B confuses the constant term with the solution set. Option C is false because a proper subset must be smaller than the other set, while these sets are equal. Option D is false because their intersection is {2, 3}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
