If the universal set U = {a, b, c, d, e} and the complement of A is Aᶜ = {b, e}, what is the value of A ∪ Aᶜ?
Answer and explanation
Correct answer: U = {a, b, c, d, e}
The complement Aᶜ contains exactly those elements of the universal set U that are not in A. Therefore, A and Aᶜ together contain every element of U and have no element outside U. Hence, the union identity is A ∪ Aᶜ = U. Here Aᶜ = {b, e}, so A = {a, c, d}; their union is {a, b, c, d, e}, which is U. Option B is only the complement, not the union.
Frequently asked questions
What is the correct answer to this question?
U = {a, b, c, d, e}
Why is this the correct answer?
The complement Aᶜ contains exactly those elements of the universal set U that are not in A. Therefore, A and Aᶜ together contain every element of U and have no element outside U. Hence, the union identity is A ∪ Aᶜ = U. Here Aᶜ = {b, e}, so A = {a, c, d}; their union is {a, b, c, d, e}, which is U. Option B is only the complement, not the union.
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.
