Which is the correct roster form of the set A = {x ∈ ℤ : x² = x}?
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Answer and explanation
Correct answer: A = {0, 1}
To find the roster form, solve the condition x² = x. Rearranging gives x² − x = 0, so x(x − 1) = 0. Therefore, x = 0 or x = 1. Both values are integers and satisfy the original equation: 0² = 0 and 1² = 1. Hence the set contains exactly these two distinct elements, so A = {0, 1}.
Frequently asked questions
What is the correct answer to this question?
A = {0, 1}
Why is this the correct answer?
To find the roster form, solve the condition x² = x. Rearranging gives x² − x = 0, so x(x − 1) = 0. Therefore, x = 0 or x = 1. Both values are integers and satisfy the original equation: 0² = 0 and 1² = 1. Hence the set contains exactly these two distinct elements, so A = {0, 1}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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