If a set has 15 proper subsets, how many elements are in its power set?
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Answer and explanation
Correct answer: 16
If a set has n elements, its power set has 2^n subsets in total. Exactly one of these subsets is the set itself, so the number of proper subsets is 2^n − 1. Given 2^n − 1 = 15, we obtain 2^n = 16. Therefore, the power set has 16 elements. The value 15 counts only proper subsets, not all subsets.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
If a set has n elements, its power set has 2^n subsets in total. Exactly one of these subsets is the set itself, so the number of proper subsets is 2^n − 1. Given 2^n − 1 = 15, we obtain 2^n = 16. Therefore, the power set has 16 elements. The value 15 counts only proper subsets, not all subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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