If U = ℤ and A = {x ∈ ℤ : x > 0}, what does Aᶜ represent?
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Answer and explanation
Correct answer: {x ∈ ℤ : x ≤ 0}
The universal set is the set of all integers. A contains the positive integers, namely integers greater than zero. The complement must therefore contain every integer that is not positive: zero and all negative integers. This set is described by x ≤ 0, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
{x ∈ ℤ : x ≤ 0}
Why is this the correct answer?
The universal set is the set of all integers. A contains the positive integers, namely integers greater than zero. The complement must therefore contain every integer that is not positive: zero and all negative integers. This set is described by x ≤ 0, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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