Truth Table/Examples/not ((p implies q) implies (not (q implies p)))

Example of Truth Table

The truth table for the WFF of propositional logic:

$\lnot \paren {\paren {p \implies q} \implies \paren {\lnot \paren {q \implies p} } }$:

can be depicted as:

$\begin{array}{c|ccc|c|cccc} \lnot & ((p & \implies & q) & \implies & (\lnot & (q & \implies & p))) \\ \hline \T & \F & \T & \F & \F & \F & \F & \T & \F \\ \F & \F & \T & \T & \T & \T & \T & \F & \F \\ \F & \T & \F & \F & \T & \F & \F & \T & \T \\ \T & \T & \T & \T & \F & \F & \T & \T & \T \\ \end{array}$

Sources

• 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.2$: Truth functions and truth tables: Exercises $3 \ \text{(b)}$