If U = {3, 6, 9, 12} and A = U, how many elements are in A′?
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Answer and explanation
Correct answer: 0
The complement of A with respect to U is defined as A′ = U − A, meaning the elements in U that are not in A. Here A and U are exactly the same set, so every element of U is already in A. No element remains after removing A from U; therefore A′ = ∅ and its cardinality is 0. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
The complement of A with respect to U is defined as A′ = U − A, meaning the elements in U that are not in A. Here A and U are exactly the same set, so every element of U is already in A. No element remains after removing A from U; therefore A′ = ∅ and its cardinality is 0. Thus 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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