If A = {0, 1}, how many elements are in P(P(A))?
Answer and explanation
Correct answer: 16
The governing rule is that a finite set with n elements has 2^n elements in its power set. Since A = {0, 1} has 2 elements, |P(A)| = 2^2 = 4. Applying the same rule again to P(A), which has 4 elements, gives |P(P(A))| = 2^4 = 16. Therefore option C is correct. The values 4 and 8 stop after the first stage or use an incorrect exponent.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The governing rule is that a finite set with n elements has 2^n elements in its power set. Since A = {0, 1} has 2 elements, |P(A)| = 2^2 = 4. Applying the same rule again to P(A), which has 4 elements, gives |P(P(A))| = 2^4 = 16. Therefore option C is correct. The values 4 and 8 stop after the first stage or use an incorrect exponent.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
