If A = {x ∈ Z : −4 ≤ x ≤ 1} and B = {x ∈ Z : −1 ≤ x ≤ 4}, what is A ∪ B?
Answer and explanation
Correct answer: {−4, −3, −2, −1, 0, 1, 2, 3, 4}
Since the elements are integers, A = {−4, −3, −2, −1, 0, 1} and B = {−1, 0, 1, 2, 3, 4}. The intervals overlap at −1, 0, and 1, and the union includes the elements from both intervals without repetition. Consequently, every integer from −4 through 4 appears in A ∪ B, giving {−4, −3, −2, −1, 0, 1, 2, 3, 4}. The other options show only the overlap or one exclusive part.
Frequently asked questions
What is the correct answer to this question?
{−4, −3, −2, −1, 0, 1, 2, 3, 4}
Why is this the correct answer?
Since the elements are integers, A = {−4, −3, −2, −1, 0, 1} and B = {−1, 0, 1, 2, 3, 4}. The intervals overlap at −1, 0, and 1, and the union includes the elements from both intervals without repetition. Consequently, every integer from −4 through 4 appears in A ∪ B, giving {−4, −3, −2, −1, 0, 1, 2, 3, 4}. The other options show only the overlap or one exclusive part.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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