If E = {x : x ∈ ℤ and x² < 10}, what is the roster form of E?
Answer and explanation
Correct answer: E = {-3, -2, -1, 0, 1, 2, 3} — E = {-3, -2, -1, 0, 1, 2, 3}
The inequality x² < 10 is equivalent to |x| < √10. Since √10 is approximately 3.16, the integers satisfying this condition range from −3 to 3. Checking them confirms that (−3)² = 9 < 10, while (−4)² = 16 > 10; the positive side is symmetric. Zero must also be included because 0² = 0 < 10. Hence E = {-3, -2, -1, 0, 1, 2, 3}, making option B correct.
Frequently asked questions
What is the correct answer to this question?
E = {-3, -2, -1, 0, 1, 2, 3} — E = {-3, -2, -1, 0, 1, 2, 3}
Why is this the correct answer?
The inequality x² < 10 is equivalent to |x| < √10. Since √10 is approximately 3.16, the integers satisfying this condition range from −3 to 3. Checking them confirms that (−3)² = 9 < 10, while (−4)² = 16 > 10; the positive side is symmetric. Zero must also be included because 0² = 0 < 10. Hence E = {-3, -2, -1, 0, 1, 2, 3}, making option B correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
