If U = {1,2,3,4,5,6} and A = {1,3,5}, how many elements are in A′?
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Answer and explanation
Correct answer: 3
The complement A′ contains the elements of the universal set U that are not in A. From U = {1,2,3,4,5,6}, remove the elements 1, 3, and 5. This gives A′ = {2,4,6}, which contains three elements. Equivalently, because A is a subset of U, n(A′) = n(U) − n(A) = 6 − 3 = 3. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The complement A′ contains the elements of the universal set U that are not in A. From U = {1,2,3,4,5,6}, remove the elements 1, 3, and 5. This gives A′ = {2,4,6}, which contains three elements. Equivalently, because A is a subset of U, n(A′) = n(U) − n(A) = 6 − 3 = 3. Therefore option B 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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