If A⊆U, what is (A′∪A)′ equal to?
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Answer and explanation
Correct answer: ∅
A set and its complement together contain every element of the universal set, so A′∪A=U. Taking the complement of both sides with respect to U gives (A′∪A)′=U′. The complement of the universal set is the empty set because no element of U lies outside U. Thus, the expression equals ∅, and option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
A set and its complement together contain every element of the universal set, so A′∪A=U. Taking the complement of both sides with respect to U gives (A′∪A)′=U′. The complement of the universal set is the empty set because no element of U lies outside U. Thus, the expression equals ∅, and 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.
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