If F₂ = {x ∈ ℕ : x² − 1 = 0}, then what is F₂?
Answer and explanation
Correct answer: {1}
Solve the equation x² − 1 = 0 by factoring: (x − 1)(x + 1) = 0. Thus the algebraic solutions are x = 1 and x = −1. However, the set-builder condition restricts x to the natural numbers. Under the usual school convention, −1 is not a natural number, whereas 1 is. Therefore only 1 belongs to F₂, so F₂ = {1}. This is a singleton set, making option B correct.
Frequently asked questions
What is the correct answer to this question?
{1}
Why is this the correct answer?
Solve the equation x² − 1 = 0 by factoring: (x − 1)(x + 1) = 0. Thus the algebraic solutions are x = 1 and x = −1. However, the set-builder condition restricts x to the natural numbers. Under the usual school convention, −1 is not a natural number, whereas 1 is. Therefore only 1 belongs to F₂, so F₂ = {1}. This is a singleton set, making option B correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
