Which of the following is the correct De Morgan’s law for complements of two sets with respect to the universal set?
Answer and explanation
Correct answer: (A∪B)ᶜ=Aᶜ∩Bᶜ
De Morgan’s law states that the complement of a union is the intersection of the complements: (A∪B)ᶜ=Aᶜ∩Bᶜ. An element is outside A∪B precisely when it is outside A and outside B, so it must belong to both Aᶜ and Bᶜ. The other statements either keep the wrong operation or incorrectly place complements, so they are not valid identities in general.
Frequently asked questions
What is the correct answer to this question?
(A∪B)ᶜ=Aᶜ∩Bᶜ
Why is this the correct answer?
De Morgan’s law states that the complement of a union is the intersection of the complements: (A∪B)ᶜ=Aᶜ∩Bᶜ. An element is outside A∪B precisely when it is outside A and outside B, so it must belong to both Aᶜ and Bᶜ. The other statements either keep the wrong operation or incorrectly place complements, so they are not valid identities in general.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
