If A and B are disjoint, then what is (A ∪ B)' equal to?
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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'. The condition that A and B are disjoint is not needed for this identity; it is true for any two subsets of the same universal set. The complement consists of elements outside both A and B.
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'. The condition that A and B are disjoint is not needed for this identity; it is true for any two subsets of the same universal set. The complement consists of elements outside both A and B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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