If A = {x : x ∈ Z and 0 < x² < 10}, which set is equal to A?
Answer and explanation
Correct answer: {-3, -2, -1, 1, 2, 3}
Because x is an integer and 0 < x² < 10, x cannot be 0, and its absolute value must be less than √10, which is approximately 3.16. The possible integer values are therefore x = -3, -2, -1, 1, 2, and 3. Their squares are 9, 4, 1, 1, 4, and 9, all strictly between 0 and 10. Hence option A gives exactly A. Option B includes 0, option C omits ±3 and includes 0, and option D includes ±4, whose square is 16.
Frequently asked questions
What is the correct answer to this question?
{-3, -2, -1, 1, 2, 3}
Why is this the correct answer?
Because x is an integer and 0 < x² < 10, x cannot be 0, and its absolute value must be less than √10, which is approximately 3.16. The possible integer values are therefore x = -3, -2, -1, 1, 2, and 3. Their squares are 9, 4, 1, 1, 4, and 9, all strictly between 0 and 10. Hence option A gives exactly A. Option B includes 0, option C omits ±3 and includes 0, and option D includes ±4, whose square is 16.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
