If A = ∅ and B = {x ∈ ℤ : x² = 0}, which statement is correct?
Answer and explanation
Correct answer: A ≠ B because B = {0}
To determine B, solve the defining condition x² = 0. The only solution is x = 0, and 0 belongs to the integers, so B = {0}. Thus B has one element, whereas A = ∅ has no elements. A singleton cannot equal the empty set, so A ≠ B. Option B is correct; C and D misclassify B, and A ignores the different contents.
Frequently asked questions
What is the correct answer to this question?
A ≠ B because B = {0}
Why is this the correct answer?
To determine B, solve the defining condition x² = 0. The only solution is x = 0, and 0 belongs to the integers, so B = {0}. Thus B has one element, whereas A = ∅ has no elements. A singleton cannot equal the empty set, so A ≠ B. Option B is correct; C and D misclassify B, and A ignores the different contents.
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.
