If U = {x : x ∈ ℤ, x² = x}, what are the elements of U?
Answer and explanation
Correct answer: U = {0, 1}
The condition defining U is x² = x. Rearranging gives x² − x = 0, which factors as x(x − 1) = 0. Therefore, x = 0 or x = 1. Both values are integers, so both satisfy the stated domain condition x ∈ ℤ. Hence U contains exactly the two elements 0 and 1, and U = {0, 1}.
Frequently asked questions
What is the correct answer to this question?
U = {0, 1}
Why is this the correct answer?
The condition defining U is x² = x. Rearranging gives x² − x = 0, which factors as x(x − 1) = 0. Therefore, x = 0 or x = 1. Both values are integers, so both satisfy the stated domain condition x ∈ ℤ. Hence U contains exactly the two elements 0 and 1, and U = {0, 1}.
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.
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