According to De Morgan's law, what is \((A\cup B)^c\) equal to?
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Answer and explanation
Correct answer: \(A^c\cap B^c\)
De Morgan’s first law states that the complement of a union equals the intersection of the complements: \((A\cup B)^c=A^c\cap B^c\). An element is outside \(A\cup B\) precisely when it is outside both A and B. Therefore, the correct answer is option A. In a Venn diagram, this is the region outside both circles.
Frequently asked questions
What is the correct answer to this question?
\(A^c\cap B^c\)
Why is this the correct answer?
De Morgan’s first law states that the complement of a union equals the intersection of the complements: \((A\cup B)^c=A^c\cap B^c\). An element is outside \(A\cup B\) precisely when it is outside both A and B. Therefore, the correct answer is option A. In a Venn diagram, this is the region outside both circles.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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