If U = {1, 2, 3, 4, 5, 6} and A′ = {1, 6}, what is A ∪ A′?
Answer and explanation
Correct answer: U
A set and its complement together contain every element of the universal set, with no element omitted. This is the fundamental identity A ∪ A′ = U. Here U is explicitly given as {1, 2, 3, 4, 5, 6}, and A′ = {1, 6}; the remaining elements form A, namely {2, 3, 4, 5}. Their union is therefore the complete universal set U. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
U
Why is this the correct answer?
A set and its complement together contain every element of the universal set, with no element omitted. This is the fundamental identity A ∪ A′ = U. Here U is explicitly given as {1, 2, 3, 4, 5, 6}, and A′ = {1, 6}; the remaining elements form A, namely {2, 3, 4, 5}. Their union is therefore the complete universal set U. Hence option A is correct.
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.
