If A has 3 elements, how many elements are in P(P(P(A)))?
Answer and explanation
Correct answer: 2²⁵⁶
For a set A with three elements, n(P(A)) = 2³ = 8. Applying the power-set operation again gives n(P(P(A))) = 2⁸ = 256. Applying it a third time gives n(P(P(P(A)))) = 2²⁵⁶. The exponent is therefore 256, not 16 or 8. Option D is only the size of P(P(A)), so it stops one power-set operation too early. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
2²⁵⁶
Why is this the correct answer?
For a set A with three elements, n(P(A)) = 2³ = 8. Applying the power-set operation again gives n(P(P(A))) = 2⁸ = 256. Applying it a third time gives n(P(P(P(A)))) = 2²⁵⁶. The exponent is therefore 256, not 16 or 8. Option D is only the size of P(P(A)), so it stops one power-set operation too early. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
