What is the roster form of the set P = {x ∈ ℤ : x² = 9}?
Answer and explanation
Correct answer: {-3, 3}
The condition x² = 9 means that x is a number whose square is 9. Since x must be an integer, we solve x² = 9 and obtain x = 3 or x = -3. Both values satisfy the condition because 3² = 9 and (-3)² = 9. Therefore, the roster form, which lists every element explicitly inside braces, is P = {-3, 3}. The order of elements in a set does not matter, so {-3, 3} and {3, -3} represent the same set.
Frequently asked questions
What is the correct answer to this question?
{-3, 3}
Why is this the correct answer?
The condition x² = 9 means that x is a number whose square is 9. Since x must be an integer, we solve x² = 9 and obtain x = 3 or x = -3. Both values satisfy the condition because 3² = 9 and (-3)² = 9. Therefore, the roster form, which lists every element explicitly inside braces, is P = {-3, 3}. The order of elements in a set does not matter, so {-3, 3} and {3, -3} represent the same set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
