If a set has 16 subsets, how many elements does it have?
Answer and explanation
Correct answer: 4
If a finite set has n elements, then each element has two choices in forming a subset: it is either included or excluded. Hence the total number of subsets is 2ⁿ. Here 2ⁿ = 16, and 16 = 2⁴. Therefore n = 4, so the set has four elements. This count includes both the empty set and the original set, as both are always subsets of a set.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
If a finite set has n elements, then each element has two choices in forming a subset: it is either included or excluded. Hence the total number of subsets is 2ⁿ. Here 2ⁿ = 16, and 16 = 2⁴. Therefore n = 4, so the set has four elements. This count includes both the empty set and the original set, as both are always subsets of a set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
