A joke has it that army recruits used to be instructed: "If it moves, salute it. If it doesn't move, paint it."
Assume that this instruction has been carried out completely in the local universe, so that everything that doesn't move has been painted.
A recruit encounters something which is not painted. What should he do, and why?
A recruit encounters something which is painted. Do we know what he or she should do? Justify your answer.
Use a truth table to prove \(( ( ( m \Rightarrow s ) \wedge ( \sim m \Rightarrow p ) ) \wedge \sim p ) \Rightarrow s\).
You are given the following two rules.
$$\begin{aligned}
& 1 \quad ( a \Rightarrow b ) \Leftrightarrow ( \sim b \Rightarrow \sim a )
& 2 \quad ( x \wedge ( x \Rightarrow y ) ) \Rightarrow y
\end{aligned}$$
Use Boolean algebra to prove that \(( ( ( m \Rightarrow s ) \wedge ( \sim m \Rightarrow p ) ) \wedge \sim p ) \Rightarrow s\).