According to De Morgan's law, what is the value of \((A\cap B)^c\)?
Answer and explanation
Correct answer: \(A^c\cup B^c\)
De Morgan's law states that the complement of an intersection is the union of the complements: \((A\cap B)^c=A^c\cup B^c\). An element is outside \(A\cap B\) whenever it is absent from at least one of the two sets. Therefore it belongs to \(A^c\) or to \(B^c\), which confirms option A. The other options either reverse the operation incorrectly or omit the complement.
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What is the correct answer to this question?
\(A^c\cup B^c\)
Why is this the correct answer?
De Morgan's law states that the complement of an intersection is the union of the complements: \((A\cap B)^c=A^c\cup B^c\). An element is outside \(A\cap B\) whenever it is absent from at least one of the two sets. Therefore it belongs to \(A^c\) or to \(B^c\), which confirms option A. The other options either reverse the operation incorrectly or omit the complement.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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