A note of the union-closed sets conjecture

Abstract

Let A = {A1,…, An} be a union-closed set. This note establishes a property which must be possessed by any smallest counterexample to the Union-Closed Sets Conjecture. Specifically, a counterexample to the conjecture with minimal n has at least three distinct elements, each of which appears in exactly (n — 1)/2 of the A1jS. © 1993, Australian Mathematical Society. All rights reserved.