According to De Morgan’s law, what is (A∪B)′ equal to?
Answer and explanation
Correct answer: A′∩B′
De Morgan’s law states that the complement of a union equals the intersection of the complements: (A∪B)′=A′∩B′. An element is outside A∪B precisely when it is outside A and outside B simultaneously. Therefore option A is correct. The union of complements would include elements outside either set, which is a different and generally larger region.
Frequently asked questions
What is the correct answer to this question?
A′∩B′
Why is this the correct answer?
De Morgan’s law states that the complement of a union equals the intersection of the complements: (A∪B)′=A′∩B′. An element is outside A∪B precisely when it is outside A and outside B simultaneously. Therefore option A is correct. The union of complements would include elements outside either set, which is a different and generally larger region.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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