If A ⊆ U, |U| = 16, and |P(A)| = 256, how many non-empty subsets of A' are there?
Answer and explanation
Correct answer: 255
For a finite set A, the power set has 2^|A| members. Since |P(A)| = 256 = 2^8, we get |A| = 8. The universal set U has 16 elements, so its complement A' has |A'| = 16 − 8 = 8 elements. A set with 8 elements has 2^8 = 256 subsets, including the empty set. Therefore, the number of non-empty subsets is 256 − 1 = 255, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
255
Why is this the correct answer?
For a finite set A, the power set has 2^|A| members. Since |P(A)| = 256 = 2^8, we get |A| = 8. The universal set U has 16 elements, so its complement A' has |A'| = 16 − 8 = 8 elements. A set with 8 elements has 2^8 = 256 subsets, including the empty set. Therefore, the number of non-empty subsets is 256 − 1 = 255, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
