Choose the correct statement about A = {x ∈ R : x² = 2}.
Answer and explanation
Correct answer: A = {-√2, √2}, and A is finite
Because the domain is the real numbers, both real square roots of 2 must be considered. Solving x² = 2 gives x = √2 or x = -√2. Therefore A = {-√2, √2}. These are two distinct real numbers, so the set has exactly two elements and is finite. A common error is to write only √2 and overlook the negative solution, even though both numbers have square 2.
Frequently asked questions
What is the correct answer to this question?
A = {-√2, √2}, and A is finite
Why is this the correct answer?
Because the domain is the real numbers, both real square roots of 2 must be considered. Solving x² = 2 gives x = √2 or x = -√2. Therefore A = {-√2, √2}. These are two distinct real numbers, so the set has exactly two elements and is finite. A common error is to write only √2 and overlook the negative solution, even though both numbers have square 2.
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.
