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  1. \item \self Model the following sentences as detailed as possible in propositional logic.
  2. \begin{enumerate}
  3. \item If a formula is unsat, it cannot be valid.
  4. \item It can be proven that there exists an infinite number of primes.
  5. \item A sentence is called declarative, if and only if it can be assigned a truth value.
  6. \end{enumerate}