If \(A=\{x:x\in\mathbb{Z},-5\le x<3\}\) and \(B=\{x:x\in\mathbb{Z},-2<x\le 6\}\), then what is \(A\cup B\)?
Answer and explanation
Correct answer: \(\{-5,-4,-3,-2,-1,0,1,2,3,4,5,6\}\)
Because the elements are integers, \(A\) contains \(-5,-4,-3,-2,-1,0,1,2\), since 3 is excluded. Set \(B\) contains \(-1,0,1,2,3,4,5,6\), since \(-2\) is excluded and 6 is included. These sets overlap at \(-1,0,1,2\), so their union contains every integer from \(-5\) through 6 without repetition. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{-5,-4,-3,-2,-1,0,1,2,3,4,5,6\}\)
Why is this the correct answer?
Because the elements are integers, \(A\) contains \(-5,-4,-3,-2,-1,0,1,2\), since 3 is excluded. Set \(B\) contains \(-1,0,1,2,3,4,5,6\), since \(-2\) is excluded and 6 is included. These sets overlap at \(-1,0,1,2\), so their union contains every integer from \(-5\) through 6 without repetition. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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