If A = {x ∈ N : x² − 1 = 0} and B = {-1, 1}, which conclusion is correct?
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Answer and explanation
Correct answer: A = {1}, so A ≠ B
The equation x² − 1 = 0 factors as (x − 1)(x + 1) = 0, giving x = 1 or x = −1. However, A is restricted to the natural numbers. Under the usual convention N = {1, 2, 3, ...}, only 1 is admitted, so A = {1}. Set B contains both −1 and 1, and therefore A ≠ B.
Frequently asked questions
What is the correct answer to this question?
A = {1}, so A ≠ B
Why is this the correct answer?
The equation x² − 1 = 0 factors as (x − 1)(x + 1) = 0, giving x = 1 or x = −1. However, A is restricted to the natural numbers. Under the usual convention N = {1, 2, 3, ...}, only 1 is admitted, so A = {1}. Set B contains both −1 and 1, and therefore A ≠ B.
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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