If A has n elements and P(A) contains 31 proper subsets, what is n?
Answer and explanation
Correct answer: 5
An n-element set has 2^n total subsets. A proper subset is any subset other than the set itself, so the number of proper subsets is 2^n − 1. Given 2^n − 1 = 31, adding 1 gives 2^n = 32 = 2^5. Therefore n = 5. For comparison, n = 4 would give 15 proper subsets and n = 6 would give 63, so option B is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
An n-element set has 2^n total subsets. A proper subset is any subset other than the set itself, so the number of proper subsets is 2^n − 1. Given 2^n − 1 = 31, adding 1 gives 2^n = 32 = 2^5. Therefore n = 5. For comparison, n = 4 would give 15 proper subsets and n = 6 would give 63, so option B is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
