If |P(A)| = 32, what is |A|?
Advertisement
Answer and explanation
Correct answer: 5
For a finite set A, the number of elements in its power set is given by |P(A)| = 2^|A|. Since |P(A)| = 32 and 32 = 2^5, we have 2^|A| = 2^5. Equality of the powers gives |A| = 5. The other options would produce 16, 64, or an enormously larger power-set size, so they cannot be correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
For a finite set A, the number of elements in its power set is given by |P(A)| = 2^|A|. Since |P(A)| = 32 and 32 = 2^5, we have 2^|A| = 2^5. Equality of the powers gives |A| = 5. The other options would produce 16, 64, or an enormously larger power-set size, so they cannot be correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement