If A = {1,2,3,4} and the universal set is U = {1,2,3,4,5,6}, what is the number of elements in P(A')?
Answer and explanation
Correct answer: 4
The complement of A relative to U consists of the elements of U that are not in A. Therefore A' = U − A = {5,6}, so |A'| = 2. Every element of A' can independently be either included in or excluded from a subset. Consequently, the power set P(A') contains 2^2 = 4 subsets: ∅, {5}, {6}, and {5,6}. Thus the correct answer is option B.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The complement of A relative to U consists of the elements of U that are not in A. Therefore A' = U − A = {5,6}, so |A'| = 2. Every element of A' can independently be either included in or excluded from a subset. Consequently, the power set P(A') contains 2^2 = 4 subsets: ∅, {5}, {6}, and {5,6}. Thus the correct answer is option B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
