 Solution

A p-value $p_i$ for $H_i$ is super-uniform under that null: ${\mathbb{P}}_{H_i}(p_i\le u)\le u$ for every $u\in [0,1]$. For the Benjamini-Hochberg procedure, order $p_{(1)}\le \cdots \le p_{(m)}$, setwith $\hat{k}=0$ if the set is empty, and reject the hypotheses whose p-values are at most $p_{(\hat{k})}$.