If A = {x ∈ ℕ : x² = 4} and B = {2}, are A and B equal?
Answer and explanation
Correct answer: Yes, because A = B = {2}
The equation x² = 4 has solutions x = 2 and x = −2 over the integers. However, the condition specifies x ∈ ℕ, so −2 is excluded. The only natural-number solution is x = 2; therefore A = {2}. Since B is also {2}, both sets contain exactly the same element and are equal. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
Yes, because A = B = {2}
Why is this the correct answer?
The equation x² = 4 has solutions x = 2 and x = −2 over the integers. However, the condition specifies x ∈ ℕ, so −2 is excluded. The only natural-number solution is x = 2; therefore A = {2}. Since B is also {2}, both sets contain exactly the same element and are equal. Option A is correct.
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.
