If H₁ = {x : x ∈ ℝ and x² = 2} and I₁ = {−√2, √2}, which statement is correct?
Answer and explanation
Correct answer: H₁ = I₁
Solving x² = 2 over the real numbers gives x = √2 or x = −√2. Therefore, the solution set is H₁ = {−√2, √2}. This is exactly the set named I₁, so H₁ = I₁. Set equality depends on having the same elements, not on how the set is written or whether its elements contain radical signs. Both sets are finite and have two elements.
Frequently asked questions
What is the correct answer to this question?
H₁ = I₁
Why is this the correct answer?
Solving x² = 2 over the real numbers gives x = √2 or x = −√2. Therefore, the solution set is H₁ = {−√2, √2}. This is exactly the set named I₁, so H₁ = I₁. Set equality depends on having the same elements, not on how the set is written or whether its elements contain radical signs. Both sets are finite and have two elements.
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.
