If A = {x ∈ Z : x² ≤ 0}, what is A?
Answer and explanation
Correct answer: {0}
For every integer x, the square x² is non-negative, so x² ≥ 0. To satisfy x² ≤ 0 at the same time, the square must be exactly zero. The only integer whose square is zero is x = 0. Consequently, the set contains one and only one element, 0, and hence A = {0}, a singleton set rather than the empty set or all of Z.
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, so x² ≥ 0. To satisfy x² ≤ 0 at the same time, the square must be exactly zero. The only integer whose square is zero is x = 0. Consequently, the set contains one and only one element, 0, and hence A = {0}, a singleton set rather than the empty set or all of Z.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
