If A = {x : x ∈ Z and x² ≤ 4}, which subset of A is not proper?
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Answer and explanation
Correct answer: {-2, -1, 0, 1, 2}
Solving x² ≤ 4 for integer x gives -2 ≤ x ≤ 2, so A = {-2, -1, 0, 1, 2}. A subset is proper only when it is strictly smaller than the original set. Option A contains every element of A and is therefore equal to A itself; it is a subset but not a proper subset. The other options omit at least one element.
Frequently asked questions
What is the correct answer to this question?
{-2, -1, 0, 1, 2}
Why is this the correct answer?
Solving x² ≤ 4 for integer x gives -2 ≤ x ≤ 2, so A = {-2, -1, 0, 1, 2}. A subset is proper only when it is strictly smaller than the original set. Option A contains every element of A and is therefore equal to A itself; it is a subset but not a proper subset. The other options omit at least one element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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