If U = {1,2,3,4,5,6,7}, A = {2,4,6}, how many elements are in Aᶜ ∩ A?
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Answer and explanation
Correct answer: 0
Relative to U, the complement of A is Aᶜ = {1,3,5,7}. No element can belong to both A and its complement: A contains {2,4,6}, while Aᶜ contains {1,3,5,7}. Therefore their intersection is Aᶜ ∩ A = ∅. The empty set has cardinality zero, so the number of elements is 0 and option A is correct.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
Relative to U, the complement of A is Aᶜ = {1,3,5,7}. No element can belong to both A and its complement: A contains {2,4,6}, while Aᶜ contains {1,3,5,7}. Therefore their intersection is Aᶜ ∩ A = ∅. The empty set has cardinality zero, so the number of elements is 0 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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