If A ⊆ U, then what is A ∩ A′ equal to?
Answer and explanation
Correct answer: ∅
The complement A′ contains elements of U that are not in A. Therefore, no element can belong to both A and A′ at the same time. Their common part, or intersection, contains no elements and is the empty set. Hence, A ∩ A′ = ∅. This identity is paired with A ∪ A′ = U and applies for complements taken relative to the same universal set U.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
The complement A′ contains elements of U that are not in A. Therefore, no element can belong to both A and A′ at the same time. Their common part, or intersection, contains no elements and is the empty set. Hence, A ∩ A′ = ∅. This identity is paired with A ∪ A′ = U and applies for complements taken relative to the same universal set U.
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.
