If the universal set is \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,4,6\}\), what is the value of \((A\cap B)^c\)?
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Answer and explanation
Correct answer: \(U\)
Set \(A\) contains only odd numbers from the universal set, whereas \(B\) contains only even numbers. Hence they have no common element and \(A\cap B=\varnothing\). The complement of the empty set relative to \(U\) is the whole universal set, so \((A\cap B)^c=\varnothing^c=U\).
Frequently asked questions
What is the correct answer to this question?
\(U\)
Why is this the correct answer?
Set \(A\) contains only odd numbers from the universal set, whereas \(B\) contains only even numbers. Hence they have no common element and \(A\cap B=\varnothing\). The complement of the empty set relative to \(U\) is the whole universal set, so \((A\cap B)^c=\varnothing^c=U\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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