If A = {x ∈ ℤ : x² = 16 and x < 0}, what is A?
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Answer and explanation
Correct answer: {-4}
Solving x² = 16 gives x = 4 or x = −4, because both numbers have square 16. The additional condition x < 0 eliminates 4 and retains −4. Thus the only integer satisfying both requirements is −4, so A = {−4}. This is a singleton set because it has exactly one element.
Frequently asked questions
What is the correct answer to this question?
{-4}
Why is this the correct answer?
Solving x² = 16 gives x = 4 or x = −4, because both numbers have square 16. The additional condition x < 0 eliminates 4 and retains −4. Thus the only integer satisfying both requirements is −4, so A = {−4}. This is a singleton set because it has exactly one element.
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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