Let N={1,2,3,...}. If U={x∈N:x≤20} and A={x∈U:x is a perfect square}, what is the value of |A'|?
Answer and explanation
Correct answer: 16
The universal set is U={1,2,...,20}, which has 20 elements. The perfect squares in this range are 1, 4, 9, and 16, so A has four elements. The complement A' contains every element of U that is not a perfect square. Therefore, |A'|=|U|−|A|=20−4=16. The complement must be taken relative to U, not to all natural numbers. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The universal set is U={1,2,...,20}, which has 20 elements. The perfect squares in this range are 1, 4, 9, and 16, so A has four elements. The complement A' contains every element of U that is not a perfect square. Therefore, |A'|=|U|−|A|=20−4=16. The complement must be taken relative to U, not to all natural numbers. Hence 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.
