If A = {x ∈ ℚ : x² = 2}, which statement about A is correct?
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Answer and explanation
Correct answer: A = ∅
The equation x² = 2 has the real solutions x = √2 and x = −√2. However, √2 is irrational, and its negative is also irrational; neither number belongs to ℚ, the set of rational numbers. Since the defining domain is ℚ, not ℝ, there are no admissible solutions. Therefore A contains no elements and A = ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The equation x² = 2 has the real solutions x = √2 and x = −√2. However, √2 is irrational, and its negative is also irrational; neither number belongs to ℚ, the set of rational numbers. Since the defining domain is ℚ, not ℝ, there are no admissible solutions. Therefore A contains no elements and A = ∅.
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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