If U = {a,b,c,d,e}, A = {a,c,e}, and B = {b,c,d}, what is (A ∪ B)′?
Answer and explanation
Correct answer: ∅
First find the union. A contains a, c, and e, while B contains b, c, and d. Together they contain every element of U, so A ∪ B = {a,b,c,d,e} = U. The complement is defined relative to U. Therefore (A ∪ B)′ = U \ (A ∪ B) = U \ U = ∅. Option B is not correct because c is already included in both A and B, so it cannot remain in the complement.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
First find the union. A contains a, c, and e, while B contains b, c, and d. Together they contain every element of U, so A ∪ B = {a,b,c,d,e} = U. The complement is defined relative to U. Therefore (A ∪ B)′ = U \ (A ∪ B) = U \ U = ∅. Option B is not correct because c is already included in both A and B, so it cannot remain in the complement.
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.
