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What is the correct roster form of A₁ = {x : x ∈ ℕ, x² − 1 = 0}?
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Answer and explanation
Correct answer: A₁ = {1}
To find the roster form, solve the defining equation: x² − 1 = 0, so x² = 1 and therefore x = −1 or x = 1. However, the condition x ∈ ℕ restricts the elements to natural numbers. Since −1 is not a natural number and 1 is a natural number, only 1 belongs to the set. Thus A₁ = {1}.
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What is the correct answer to this question?
A₁ = {1}
Why is this the correct answer?
To find the roster form, solve the defining equation: x² − 1 = 0, so x² = 1 and therefore x = −1 or x = 1. However, the condition x ∈ ℕ restricts the elements to natural numbers. Since −1 is not a natural number and 1 is a natural number, only 1 belongs to the set. Thus A₁ = {1}.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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