If A = ∅ and B = {x ∈ ℤ : x² + 1 = 0}, what is the conclusion?
Answer and explanation
Correct answer: A = B
For every integer x, x² is non-negative, so x² + 1 is at least 1 and can never equal 0. Thus the equation x² + 1 = 0 has no integer solution, which means B contains no elements. Therefore B is the empty set, just like A. Since two sets are equal when they have exactly the same elements, A = B. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
For every integer x, x² is non-negative, so x² + 1 is at least 1 and can never equal 0. Thus the equation x² + 1 = 0 has no integer solution, which means B contains no elements. Therefore B is the empty set, just like A. Since two sets are equal when they have exactly the same elements, A = B. Hence, 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.
