show using truth tables, that the statement "if P then Q" is logically equivalent to the statement "not P or Q"
fill out the table and observe that the truth values for both expressions are the same in each corresponding entry:
$\displaystyle \begin{array}{|c|c|c|c|c|}
\hline \bold{P} & \bold{Q} & \neg \bold{ P} & \bold{P} \implies \bold{Q} & \bold{\neg P \vee Q} \\
\hline T & T & & & \\
\hline T & F & & & \\
\hline F & T & & & \\
\hline F & F & & & \\
\hline \end{array}$