Truth Table/Examples/((not p) and q) implies ((not q) and r)
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Example of Truth Table
The truth table for the WFF of propositional logic:
- $\paren {\paren {\lnot p} \land q} \implies \paren {\paren {\lnot q} \land r}$:
can be depicted as:
$\begin{array}{|cccc|c|cccc|} \hline ((\lnot & p) & \land & q) & \implies & ((\lnot & q) & \land & r) \\ \hline \T & \F & \F & \F & \T & \T & \F & \F & \F \\ \T & \F & \F & \F & \T & \T & \F & \T & \T \\ \T & \F & \T & \T & \F & \F & \T & \F & \F \\ \T & \F & \T & \T & \T & \F & \T & \T & \T \\ \F & \T & \F & \F & \T & \T & \F & \T & \F \\ \F & \T & \F & \F & \T & \T & \F & \T & \T \\ \F & \T & \F & \T & \T & \F & \T & \F & \F \\ \F & \T & \F & \T & \T & \F & \T & \F & \T \\ \hline \end{array}$
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 $3 \ \text{(g)}$