What is the roster form of Q₁ = {x : x ∈ ℤ, x² < 10, and x is even}?
Answer and explanation
Correct answer: Q₁ = {−2, 0, 2}
The inequality x² < 10 implies −√10 < x < √10. Since √10 is slightly greater than 3, the possible integer values are −3, −2, −1, 0, 1, 2, and 3. Applying the additional condition that x must be even leaves only −2, 0, and 2. Hence the roster form is {−2, 0, 2}; values such as ±4 do not satisfy the inequality.
Frequently asked questions
What is the correct answer to this question?
Q₁ = {−2, 0, 2}
Why is this the correct answer?
The inequality x² < 10 implies −√10 < x < √10. Since √10 is slightly greater than 3, the possible integer values are −3, −2, −1, 0, 1, 2, and 3. Applying the additional condition that x must be even leaves only −2, 0, and 2. Hence the roster form is {−2, 0, 2}; values such as ±4 do not satisfy the inequality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
