\item \lect
Given the following execution word $w$ of a Kripke structure. Evaluate the
formula $\varphi$ on $w$. Evaluate each sub-formula for any execution step using the
provided table.

\begin{itemize}
    \item $w = \{\}, \{a\}, \{ \}, \{a,b,c\}, \{a\}, \{a,b\}, ( \{a\} ,  \{a,c\}, \{a,c\})^\omega$
    \item  $\varphi = \glob \event a \imp (\event  \glob \neg b \wedge c )$
\end{itemize}

  \begin{ltltabular}{9}
    \ltlSteps{6}{3}
    \ltlTrace{a}{0|1|0|1|1|1 |1|1|1}
    \ltlTrace{b}{0|0|0|1|0|1 |0|0|0}
    \ltlTrace{c}{0|0|0|1|0|0 |0|1|1}
    \hline
    \hline
    \ltlFormula{$\glob \event a$}
               {\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}}
    \ltlFormula{$\event \glob \neg b$}
               {\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}}
    \ltlFormula{$\event \glob \neg b \wedge c$}
               {\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}}
    \ltlFormula{$\glob \event a \imp (\event  \glob \neg b \wedge c )$}
               {\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}|\ws{1cm}}
  \end{ltltabular} 
  \newline