If the universal set is U = {1,2,3,...,10}, A = {2,4,6,8,10}, and B = {1,2,3,4,5}, what is (Aᶜ ∪ B)ᶜ?
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Answer and explanation
Correct answer: {6,8,10}
The complement of A with respect to U is Aᶜ = {1,3,5,7,9}. Taking the union with B gives Aᶜ ∪ B = {1,2,3,4,5,7,9}. The elements of U not present in this union are {6,8,10}, so (Aᶜ ∪ B)ᶜ = {6,8,10}. This also follows from De Morgan’s law: (Aᶜ ∪ B)ᶜ = A ∩ Bᶜ.
Frequently asked questions
What is the correct answer to this question?
{6,8,10}
Why is this the correct answer?
The complement of A with respect to U is Aᶜ = {1,3,5,7,9}. Taking the union with B gives Aᶜ ∪ B = {1,2,3,4,5,7,9}. The elements of U not present in this union are {6,8,10}, so (Aᶜ ∪ B)ᶜ = {6,8,10}. This also follows from De Morgan’s law: (Aᶜ ∪ B)ᶜ = A ∩ Bᶜ.
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.
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