# Difference between revisions of "Frankl's union-closed conjecture"

A family $\mathcal{A}$ of sets is called union closed if $A\cup B\in\mathcal{A}$ whenever $A\in\mathcal{A}$ and $B\in\mathcal{A}$. Frankl's conjecture is a disarmingly simple one: if $\mathcal{A}$ is a union-closed family of n sets, then must there be an element that belongs to at least n/2 of the sets? The problem has been open for decades, despite the attention of several people.