If U = {1, 2, ..., 15} and A = {3, 6, 9, 12, 15}, what is n(P(A'))?
Advertisement
Answer and explanation
Correct answer: 1024
The universal set U contains 15 elements, while A contains the five multiples of 3 from 1 to 15. Therefore, the complement A' contains the remaining 15 − 5 = 10 elements. A set with n elements has 2^n subsets, so its power set contains 2^10 = 1024 elements. Hence, n(P(A')) = 1024, which is option A.
Frequently asked questions
What is the correct answer to this question?
1024
Why is this the correct answer?
The universal set U contains 15 elements, while A contains the five multiples of 3 from 1 to 15. Therefore, the complement A' contains the remaining 15 − 5 = 10 elements. A set with n elements has 2^n subsets, so its power set contains 2^10 = 1024 elements. Hence, n(P(A')) = 1024, which is option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement