Sharpened Bonferroni Inequalities

Improved Bonferroni inequalities obtained by I. Tomescu (1986, J. Combin. Theory Ser. B41, 209-217) are sharpened and the new bounds are shown to be best possible. Similar bounds are given for measures of complemented distributive lattices. Finally, algorithms for finding the hypergraph which gives the sharpest bound are discussed.