Please help with the following proof:
Let $S =$ {$A_1, (A_1\to A_2), (A_2 \to A_3), (A_3 \to A_4), (¬A_4)$}. Show that any proper subset of $S$ is satisfiable.
Just looking at the set S, I can see that the statement is true. The only way I see of proving this is to go case by case. Does anyone see a better way of proving this? Also, please share any general tips for proving this statement for different values of $S$.