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