If U = {1, 2, ..., 20} and A is the set of all prime numbers in U, what is n(P(A'))?
Advertisement
Answer and explanation
Correct answer: 4096
The primes from 1 through 20 are 2, 3, 5, 7, 11, 13, 17, and 19, so n(A) = 8. Because the complement is relative to U, n(A') = 20 − 8 = 12. Applying the power-set rule, a 12-element set has 2¹² = 4096 subsets. Therefore option A is correct; 256, 1024, and 8192 are incorrect powers of two for this problem.
Frequently asked questions
What is the correct answer to this question?
4096
Why is this the correct answer?
The primes from 1 through 20 are 2, 3, 5, 7, 11, 13, 17, and 19, so n(A) = 8. Because the complement is relative to U, n(A') = 20 − 8 = 12. Applying the power-set rule, a 12-element set has 2¹² = 4096 subsets. Therefore option A is correct; 256, 1024, and 8192 are incorrect powers of two for this problem.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement