If A = {x ∈ ℤ : −2 ≤ x < 5} and B = {x ∈ ℤ : x² ≤ 9}, then what is A − B?
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Answer and explanation
Correct answer: A − B = {4}
Since x is an integer and −2 ≤ x < 5, A = {−2, −1, 0, 1, 2, 3, 4}. The inequality x² ≤ 9 is equivalent to −3 ≤ x ≤ 3, so B = {−3, −2, −1, 0, 1, 2, 3}. Set difference A − B retains members of A that are absent from B. Every member except 4 is removed, giving {4}; therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
A − B = {4}
Why is this the correct answer?
Since x is an integer and −2 ≤ x < 5, A = {−2, −1, 0, 1, 2, 3, 4}. The inequality x² ≤ 9 is equivalent to −3 ≤ x ≤ 3, so B = {−3, −2, −1, 0, 1, 2, 3}. Set difference A − B retains members of A that are absent from B. Every member except 4 is removed, giving {4}; 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).
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