A question about the polynomial hierarchy Why does $\Pi_i^p \subseteq \Sigma_i^p$ imply $\Pi_i^p = \Sigma_i^p$?
Hint: $L \in \Sigma_i^p$ iff $\overline{L} \in \Pi_i^p$. (Here $\overline{L}$ is the complement of $L$.)