If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 3, 5, 7}, how many elements are in A′?
Answer and explanation
Correct answer: 4
The complement A′ consists of the elements of U that are absent from A. From U = {1, 2, 3, 4, 5, 6, 7, 8}, remove 1, 3, 5, and 7. This gives A′ = {2, 4, 6, 8}, which contains four elements. Equivalently, because U has 8 elements and A has 4 elements, n(A′) = n(U) − n(A) = 8 − 4 = 4. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The complement A′ consists of the elements of U that are absent from A. From U = {1, 2, 3, 4, 5, 6, 7, 8}, remove 1, 3, 5, and 7. This gives A′ = {2, 4, 6, 8}, which contains four elements. Equivalently, because U has 8 elements and A has 4 elements, n(A′) = n(U) − n(A) = 8 − 4 = 4. Therefore, option C 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.
