If A = {x ∈ Z : x² = 0} and B = ∅, which statement is correct?
Answer and explanation
Correct answer: A = {0} and A ≠ B
Solving x² = 0 gives x = 0, and 0 is an integer. Therefore A contains exactly one element: A = {0}. The empty set B = ∅ contains no elements. Since {0} has one element while ∅ has none, A and B are not equal. This also illustrates the important difference between a singleton set containing zero and the empty set containing nothing.
Frequently asked questions
What is the correct answer to this question?
A = {0} and A ≠ B
Why is this the correct answer?
Solving x² = 0 gives x = 0, and 0 is an integer. Therefore A contains exactly one element: A = {0}. The empty set B = ∅ contains no elements. Since {0} has one element while ∅ has none, A and B are not equal. This also illustrates the important difference between a singleton set containing zero and the empty set containing nothing.
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.
