Which option represents a set equal to {0, 1}?
Answer and explanation
Correct answer: {x ∈ ℤ : x² = x}
For option A, x² = x becomes x² − x = 0, or x(x − 1) = 0. Thus the integer solutions are x = 0 and x = 1, so the described set is exactly {0, 1}. Option B gives only {−1, 1} if interpreted over integers, but its stated natural domain gives {1}; option C gives {−1, 1}, and option D is infinite.
Frequently asked questions
What is the correct answer to this question?
{x ∈ ℤ : x² = x}
Why is this the correct answer?
For option A, x² = x becomes x² − x = 0, or x(x − 1) = 0. Thus the integer solutions are x = 0 and x = 1, so the described set is exactly {0, 1}. Option B gives only {−1, 1} if interpreted over integers, but its stated natural domain gives {1}; option C gives {−1, 1}, and option D is infinite.
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.
