If A = {x ∈ ℤ : x² < 0}, what is n(A)?
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Answer and explanation
Correct answer: 0
For every integer x, the square x² is non-negative: it is either positive when x ≠ 0 or equal to 0 when x = 0. Therefore no integer can satisfy x² < 0. The set A has no elements, so A is the empty set. The cardinality of the empty set is n(A) = 0, making option A correct.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
For every integer x, the square x² is non-negative: it is either positive when x ≠ 0 or equal to 0 when x = 0. Therefore no integer can satisfy x² < 0. The set A has no elements, so A is the empty set. The cardinality of the empty set is n(A) = 0, making option A 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.
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