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Diffstat (limited to 'Assignment1/exercises.tex')
| -rw-r--r-- | Assignment1/exercises.tex | 3 |
1 files changed, 2 insertions, 1 deletions
diff --git a/Assignment1/exercises.tex b/Assignment1/exercises.tex index 9126427..5849c84 100644 --- a/Assignment1/exercises.tex +++ b/Assignment1/exercises.tex @@ -17,7 +17,7 @@ \item $(\lnot (a \land b)) \land (\lnot (\lnot a \land \lnot b))$. \item $a \Uop a$. \item $a \land ((b \Uop a) \lor \lnot(b \Uop a))$. - \item $\text{false} \rightarrow (a \Uop b)$. + \item $\bot \rightarrow (a \Uop b)$. \end{enumerate} \end{multicols} @@ -33,6 +33,7 @@ \end{exercise} \begin{exercise} + \label{ex:dual-modalities} On page~\pageref{pltl:dual-modalities}, we discussed informally why the dual modalities $\lozenge^{-1}\square^{-1}\phi$ and $\square^{-1}\lozenge^{-1}\phi$ are both equivalent to \enquote{at the first moment in time, $\phi$}. Prove this formally, i.e.\ that for all infinite words $\sigma$ and $i\in\mathbb N$, \[ |