\begin{enumerate}
    \item $u:$ \quad The formula is unsat. \\
          $v:$ \quad The formula is valid.
          $$ u \imp \neg v $$
    \item $P:$ \quad It can be proven that there exist an infinite number of primes.
          $$ P $$
    \item $d:$ \quad The sentence is a declarative sentence. \\
          $t:$ \quad A truth value can be assigned to the sentence.
          $$ d \biimp t $$
\end{enumerate}