Truth Table/Examples/(p and q) implies r

Example of Truth Table

The truth table for the WFF of propositional logic:

$\paren {p \land q} \implies r$:

can be depicted as:

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

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 $3 \ \text{(d)}$