  Let F be a finite union-closed family of sets whose largest set contains n
elements. In \cite{Wojcik92}, Wojcik defined the density of F to be the ratio
of the average set size of F to n and conjectured that the minimum density over
all union-closed families whose largest set contains n elements is (1 +
o(1))\log_2(n)/(2n) as n approaches infinity. We use a result of Reimer
\cite{Reimer03} to show that the density of F is always at least log_2(n)/(2n),
verifying Wojcik's conjecture. As a corollary we show that for n \geq 16, some
element must appear in at least \sqrt{(\log_2(n))/n}(|F|/2) sets of F.
