We use the following Boolean variables:
\begin{itemize}
    \item $a$ represents ``The robot visits region A''
    \item $b$ represents ``The robot visits region B''    
    \item $c$ represents ``The robot visits region C''  
\end{itemize}

\begin{itemize}
    \item $\varphi_1 \coloneqq E(GF a \wedge GF c)$
    \item $\varphi_2 \coloneqq A (GF a \wedge FG \neg c)$
    \item $\varphi_3 \coloneqq A (GF a \rightarrow GF c)$
\end{itemize}