If U = {x ∈ N : 1 ≤ x ≤ 18} and A = {x ∈ U : 4 divides x}, how many elements are in the complement A′?
Advertisement
Answer and explanation
Correct answer: 14
The universal set U contains the integers 1 through 18, so it has 18 elements. The elements divisible by 4 are A = {4, 8, 12, 16}, giving |A| = 4. The complement A′ contains the elements of U that are not in A. Hence |A′| = |U| − |A| = 18 − 4 = 14, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The universal set U contains the integers 1 through 18, so it has 18 elements. The elements divisible by 4 are A = {4, 8, 12, 16}, giving |A| = 4. The complement A′ contains the elements of U that are not in A. Hence |A′| = |U| − |A| = 18 − 4 = 14, so 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.
Advertisement