How many elements are in A = {x : x ∈ ℤ, x² = 1}?
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Answer and explanation
Correct answer: 2
To find the members of A, solve x² = 1 over the integers. Factoring gives (x − 1)(x + 1) = 0, so x = 1 or x = −1. Both solutions are integers and both satisfy the condition. Therefore A = {−1, 1}, which contains two distinct elements. Thus the correct answer is option C.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
To find the members of A, solve x² = 1 over the integers. Factoring gives (x − 1)(x + 1) = 0, so x = 1 or x = −1. Both solutions are integers and both satisfy the condition. Therefore A = {−1, 1}, which contains two distinct elements. Thus the correct answer is option C.
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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