Which is the roster form of A = {x ∈ Z : x² ≤ 16 and x is not prime}?
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Answer and explanation
Correct answer: A = {-4, -3, -2, -1, 0, 1, 4}
The inequality x² ≤ 16 gives -4 ≤ x ≤ 4, so the integer candidates are -4, -3, -2, -1, 0, 1, 2, 3, and 4. Among these, the only prime numbers are 2 and 3. Removing them leaves -4, -3, -2, -1, 0, 1, and 4. Negative integers, zero, and one are not prime by the definition of a prime number.
Frequently asked questions
What is the correct answer to this question?
A = {-4, -3, -2, -1, 0, 1, 4}
Why is this the correct answer?
The inequality x² ≤ 16 gives -4 ≤ x ≤ 4, so the integer candidates are -4, -3, -2, -1, 0, 1, 2, 3, and 4. Among these, the only prime numbers are 2 and 3. Removing them leaves -4, -3, -2, -1, 0, 1, and 4. Negative integers, zero, and one are not prime by the definition of a prime number.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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