A collection of subsets of {1,2, …, n} has the property that each pair of subsets has at least o

Name: A collection of subsets of {1,2, …, n} has the property that each pair of subsets has at least one element in common. Prove that there are at most 2^n-1 subsets in the collection.
Uploaded: 2024-05-10T11:55:25-08:00
Duration: 4 min 23 s
Channel: Adi S
Description: A collection of subsets of {1,2, …, n} has the property that each pair of subsets has at least one element in common. Prove that there are at most 2^n-1 subsets in the collection.

Question

Narendra Kumar · Accepted Answer

1. If there is a subset $A$ in the collection that contains all elements from ${1, 2, ldots, n

Question

A collection of subsets of $\{1,2, \ldots, n\}$ has the property that each pair of subsets has at least one element in common. Prove that there are at most $2^{n-1}$ subsets in the collection.

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