If A = {x ∈ ℤ : x² < 10 and x > -3}, what is A in roster form?
Advertisement
Answer and explanation
Correct answer: A = {-2, -1, 0, 1, 2, 3}
The variable x is restricted to integers. The inequality x² < 10 allows the integers -3 through 3, because 3² = 9 is less than 10 but 4² = 16 is not. The additional condition x > -3 excludes -3 itself, while -2, -1, 0, 1, 2, and 3 satisfy both conditions. Hence A = {-2, -1, 0, 1, 2, 3}.
Frequently asked questions
What is the correct answer to this question?
A = {-2, -1, 0, 1, 2, 3}
Why is this the correct answer?
The variable x is restricted to integers. The inequality x² < 10 allows the integers -3 through 3, because 3² = 9 is less than 10 but 4² = 16 is not. The additional condition x > -3 excludes -3 itself, while -2, -1, 0, 1, 2, and 3 satisfy both conditions. Hence A = {-2, -1, 0, 1, 2, 3}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
Advertisement