What is the correct identification of A = {x ∈ ℝ : x² − 2x + 1 = 0}?
Answer and explanation
Correct answer: {1}, a singleton finite set
Rewrite the equation as x² − 2x + 1 = (x − 1)² = 0. Hence x = 1 is the only real solution. Although the root is repeated algebraically, a set does not record repetition; it contains the element 1 only once. Therefore A = {1}, which is a singleton and a finite set. Option B is correct.
Frequently asked questions
What is the correct answer to this question?
{1}, a singleton finite set
Why is this the correct answer?
Rewrite the equation as x² − 2x + 1 = (x − 1)² = 0. Hence x = 1 is the only real solution. Although the root is repeated algebraically, a set does not record repetition; it contains the element 1 only once. Therefore A = {1}, which is a singleton and a finite set. Option B 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.
