If A = {4, 5}, how many elements are in P(P(A))?
Answer and explanation
Correct answer: 16
Set A has two elements, so its power set contains 2^2 = 4 subsets: the empty set, the two singleton subsets, and A itself. The set P(A) therefore has 4 elements. Taking the power set once more gives |P(P(A))| = 2^4 = 16. The exponent in the second step is 4 because P(A), rather than A, is the set whose subsets are being counted.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Set A has two elements, so its power set contains 2^2 = 4 subsets: the empty set, the two singleton subsets, and A itself. The set P(A) therefore has 4 elements. Taking the power set once more gives |P(P(A))| = 2^4 = 16. The exponent in the second step is 4 because P(A), rather than A, is the set whose subsets are being counted.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
