If n(P(A)) = 64, what is n(A)?
Advertisement
Answer and explanation
Correct answer: 6
For a finite set A, the number of elements in its power set is given by n(P(A)) = 2^n(A). Here 2^n(A) = 64. Since 64 = 2^6, the exponent must be n(A) = 6. The alternatives do not work: 2^4 = 16, 2^5 = 32, and 2^8 = 256. Therefore the set A contains six elements.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
For a finite set A, the number of elements in its power set is given by n(P(A)) = 2^n(A). Here 2^n(A) = 64. Since 64 = 2^6, the exponent must be n(A) = 6. The alternatives do not work: 2^4 = 16, 2^5 = 32, and 2^8 = 256. Therefore the set A contains six elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement