If U = {x : x ∈ ℕ, 1 ≤ x ≤ 20} and A = {x ∈ U : x > 12}, what is n(A′)?
Answer and explanation
Correct answer: 12
The universal set is U = {1, 2, 3, ..., 20}. Since A contains the elements greater than 12, A = {13, 14, 15, 16, 17, 18, 19, 20}, which has 8 elements. The complement A′ contains all elements of U that are not in A, namely {1, 2, ..., 12}. Therefore, n(A′) = 20 − 8 = 12. The number 12 is not included in A because the condition is x > 12, not x ≥ 12.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The universal set is U = {1, 2, 3, ..., 20}. Since A contains the elements greater than 12, A = {13, 14, 15, 16, 17, 18, 19, 20}, which has 8 elements. The complement A′ contains all elements of U that are not in A, namely {1, 2, ..., 12}. Therefore, n(A′) = 20 − 8 = 12. The number 12 is not included in A because the condition is x > 12, not x ≥ 12.
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.
