If U = {1, 2, …, 24} and A′ = {1, 5, 7, 11, 13, 17, 19, 23}, how many elements are in A?
Answer and explanation
Correct answer: 16
The universal set U contains all integers from 1 through 24, so |U| = 24. The given complement A′ contains 8 elements. Since A and A′ are disjoint and together make U, |A| + |A′| = |U|. Therefore, |A| = 24 − 8 = 16. Hence, option C is correct. This uses the complement cardinality property for a finite universal set.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The universal set U contains all integers from 1 through 24, so |U| = 24. The given complement A′ contains 8 elements. Since A and A′ are disjoint and together make U, |A| + |A′| = |U|. Therefore, |A| = 24 − 8 = 16. Hence, option C is correct. This uses the complement cardinality property for a finite universal set.
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.
