If A = {x ∈ ℝ : x² = 3} and B = {√3, −√3}, what is the correct statement about A and B?
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Answer and explanation
Correct answer: A = B
Solving x² = 3 over the real numbers gives x = √3 or x = −√3. Although √3 is irrational, it is still a real number, so both solutions satisfy the stated domain x ∈ ℝ. Consequently, A = {√3, −√3}, which is exactly B. The fact that the roots are irrational does not exclude them from a real-number set.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Solving x² = 3 over the real numbers gives x = √3 or x = −√3. Although √3 is irrational, it is still a real number, so both solutions satisfy the stated domain x ∈ ℝ. Consequently, A = {√3, −√3}, which is exactly B. The fact that the roots are irrational does not exclude them from a real-number set.
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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