The union-closed set conjecture is true

TL;DR

This paper proves the long-standing union-closed set conjecture, confirming that in any finite union-closed family with non-empty sets, some element appears in at least half of the sets.

Contribution

It provides a rigorous proof of the union-closed set conjecture, resolving a problem posed by Peter Frankl in the 1970s.

Findings

Confirmed the union-closed set conjecture for all finite families

Established that some element appears in at least half of the sets

Resolved a long-standing open problem in combinatorics

Abstract

We prove that the conjecture made by Peter Frankl in the late 1970s is true. In other words for every finite union-closed family which contains a non?empty set, there is an element that belongs to at least half of its m