A Combinatorial Approach to Improved Bonferroni Inequalities

We reprove an important case of a recent topological result on improved Bonferroni inequalities due to Naiman and Wynn in a purely combinatorial manner. Our statement and proof involves the combinatorial concept of non-evasiveness instead of the topological concept of contractibility. In contradistinction to the proof of Naiman and Wynn, our proof does not require knowledge of simplicial homology theory.