For this question, we take ${}^{{?}^{?}}$ to abbreviate not$($not$),$ and $vv$ to abbreviate not$.$

$($a$)$ Prove that if $$ and $$ are formulas of a first$-$order language $L,$ and $I=(A,)$ is an interpretation of $L,$ then $I||==(vv)$ iff $I||==$ or $I||==.$

$($b$)$ Prove that if $$ and $$ are formulas of a first$-$order language $L,$ and $I=(A,)$ is an interpretation of $L,$ then $I||==({}^{{?}^{?}})$ iff $I||==$ and $I||==.$