If A = {x ∈ Z : −3 ≤ x < 4} and B = {x ∈ Z : x² ≤ 4}, what is A \ B?
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Answer and explanation
Correct answer: {−3, 3}
For integer x with −3 ≤ x < 4, A = {−3, −2, −1, 0, 1, 2, 3}. The inequality x² ≤ 4 gives −2 ≤ x ≤ 2, so B = {−2, −1, 0, 1, 2}. Subtracting B from A removes the five central elements and leaves the endpoints −3 and 3. Hence A \ B = {−3, 3}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{−3, 3}
Why is this the correct answer?
For integer x with −3 ≤ x < 4, A = {−3, −2, −1, 0, 1, 2, 3}. The inequality x² ≤ 4 gives −2 ≤ x ≤ 2, so B = {−2, −1, 0, 1, 2}. Subtracting B from A removes the five central elements and leaves the endpoints −3 and 3. Hence A \ B = {−3, 3}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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