If A = {x ∈ ℝ : x² − 6x + 9 = 0} and B = {3, 3, 3}, which statement is correct?
Answer and explanation
Correct answer: A = B
Factor the equation as x² − 6x + 9 = (x − 3)² = 0. Thus, its only solution is x = 3, so A = {3}. In set notation, repeated entries are not counted more than once; therefore {3, 3, 3} is also simply {3}. Both sets contain exactly the same element, so A and B are equal. Repetition does not create additional set elements.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Factor the equation as x² − 6x + 9 = (x − 3)² = 0. Thus, its only solution is x = 3, so A = {3}. In set notation, repeated entries are not counted more than once; therefore {3, 3, 3} is also simply {3}. Both sets contain exactly the same element, so A and B are equal. Repetition does not create additional set elements.
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.
