A Note on the Union-closed Sets Conjecture

Mohammad Javad Moghaddas Mehr

Published 2023-09-04Version 1

Let $M=(m_{ij})$ be a binary matrix of size $n \times m$ with distinct rows where its rows are closed under logical operators such as "$\boldsymbol{\rightarrow}$", "$\boldsymbol{\land}$", "$\boldsymbol{\neg}$", etc. In this article, we explore whether, in each case, there exists a column that has an equal or greater number of ones than zeros.