Suppose we expand our language by adding a "neither...nor" operator darr :

Syntax: if A and B are wffs$,$ then $(AdarrB)$ is a wff$.$

Semantics: If A and B are wffs$,$ then $v(AdarrB)=1$ iff $v(A)=0$ and $v(B)=0$

The tableaux rules for this operator are:

$($a$)$ Prove the Soundness Lemma for darr and notdarr.

$($b$)$ Prove the Completeness Lemma for darr and notdarr.