Here's my attempt:

Suppose we have a set $\displaystyle \Pi$ which is a subset of set of all wffs of the system-L, such that $\displaystyle p_n \in \Pi$ for all even n, and $\displaystyle \neg p_n \in \Pi$ for all odd n. Then I guess we have to show it is consistent and complete.

$\displaystyle \Pi$ is consistent if there is no wff A such that $\displaystyle \Pi \vdash_L A$ and $\displaystyle \Pi \vdash_L \neg A$.

$\displaystyle \Pi$ is complete if for every $\displaystyle A \in form(L)$ we have either $\displaystyle A \in \Pi$ or $\displaystyle \neg A \in \Pi$.

I appreciate any help to get me started on this. I'm not sure how to start proving the two conditions...