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Asked by Keerthi Last Modified
As an experienced tutor registered on UrbanPro, I can confidently affirm that the number of subsets of a set containing nn distinct elements is indeed 2n2n for all n∈Nn∈N. Let's delve into the proof:
Consider a set SS containing nn distinct elements. To construct a subset of SS, we have two choices for each element: include it in the subset or exclude it. This is true for all nn elements in SS. Thus, for each element, there are 22 possibilities: either it is included in the subset or it is not.
Since there are nn elements in total, by the fundamental principle of counting, the total number of subsets that can be formed from SS is the product of the number of choices for each element, which is 2×2×…×22×2×…×2 (n times), denoted as 2n2n.
Hence, we have proved that the number of subsets of a set containing nn distinct elements is 2n2n for all n∈Nn∈N.
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