If U = {1, 2, 3, 4, 5, 6} and A = {1, 2}, what is n(A′), the number of elements in the complement of A?
Advertisement
Answer and explanation
Correct answer: 4
The complement A′ contains the elements of U that are not in A. Since A is a subset of U, we can use n(A′) = n(U) − n(A). Here n(U) = 6 and n(A) = 2, so n(A′) = 6 − 2 = 4. Directly, A′ = {3, 4, 5, 6}, which confirms the result. Therefore option C is correct; option D counts all elements of U without removing A.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The complement A′ contains the elements of U that are not in A. Since A is a subset of U, we can use n(A′) = n(U) − n(A). Here n(U) = 6 and n(A) = 2, so n(A′) = 6 − 2 = 4. Directly, A′ = {3, 4, 5, 6}, which confirms the result. Therefore option C is correct; option D counts all elements of U without removing A.
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.
Advertisement