If \(U=\mathbb{R}\), \(A=(-5,2]\), and \(B=[-1,6)\), what is \((A\cap B)'\)?
Answer and explanation
Correct answer: \((- ,-1)\cup(2, )\)
The common part of the two intervals is found by taking the larger lower bound and the smaller upper bound. Thus \(A\cap B=[-1,2]\): both endpoints are included because -1 belongs to both intervals and 2 also belongs to both. The complement in \(\mathbb{R}\) excludes this closed interval, giving \((- ,-1)\cup(2, )\).
Frequently asked questions
What is the correct answer to this question?
\((- ,-1)\cup(2, )\)
Why is this the correct answer?
The common part of the two intervals is found by taking the larger lower bound and the smaller upper bound. Thus \(A\cap B=[-1,2]\): both endpoints are included because -1 belongs to both intervals and 2 also belongs to both. The complement in \(\mathbb{R}\) excludes this closed interval, giving \((- ,-1)\cup(2, )\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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