If A = {x : x ∈ ℤ, |x| ≤ 3} and B = {x : x ∈ ℤ, x² − 1 = 0}, what is A \ B?
Answer and explanation
Correct answer: {−3, −2, 0, 2, 3}
The condition |x| ≤ 3, with x an integer, gives A = {−3, −2, −1, 0, 1, 2, 3}. For B, x² − 1 = 0 means x² = 1, so x = −1 or x = 1; hence B = {−1, 1}. The difference A \ B contains the elements of A that are not in B. Removing −1 and 1 from A leaves {−3, −2, 0, 2, 3}. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
{−3, −2, 0, 2, 3}
Why is this the correct answer?
The condition |x| ≤ 3, with x an integer, gives A = {−3, −2, −1, 0, 1, 2, 3}. For B, x² − 1 = 0 means x² = 1, so x = −1 or x = 1; hence B = {−1, 1}. The difference A \ B contains the elements of A that are not in B. Removing −1 and 1 from A leaves {−3, −2, 0, 2, 3}. Therefore 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).
