If A = {x : x ∈ ℤ and x² = 1} and B = {−1, 1}, which statement is true?
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Answer and explanation
Correct answer: A = B
The condition x² = 1 can be factored as (x − 1)(x + 1) = 0. Therefore x = 1 or x = −1. Both values are integers, so the set defined by the rule is A = {−1, 1}. This is exactly the set given as B. Hence A = B. The other options omit one valid solution or incorrectly claim that there are no solutions.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The condition x² = 1 can be factored as (x − 1)(x + 1) = 0. Therefore x = 1 or x = −1. Both values are integers, so the set defined by the rule is A = {−1, 1}. This is exactly the set given as B. Hence A = B. The other options omit one valid solution or incorrectly claim that there are no solutions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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