How to use a formal proof in order to show that an argument is valid.
How to use a truth table to show that an argument is valid.
J-“Juliet takes the drug”; C-“Juliet is caught”; R-“Romeo thinks Juliet is dead”; D(R)-“Romeo is dead”; and D(J)-“Juliet is dead”.
Argument:
$\displaystyle \begin{array}{l}
\sim J \to C \\
J \to R \\
R \to D(R) \\
\underline {D(R) \to D(J)} \\
\sim C \to \left( {D(R)D(J)} \right) \\
\end{array}$
Proof
$\displaystyle \begin{array}{l}
\sim C \to J\quad (1) \\
\sim C \to R \\
\sim C \to D(R) \\
\sim C \to D(J) \\
C \vee D(R) \\
C \vee D(J) \\
\left( {C \vee D(R)} \right) \wedge \left( {C \vee D(J)} \right) \\
\underline {C \vee \left( {D(R) \wedge D(J)} \right)} \\
\sim C \to \left( {D(R) \wedge D(J)} \right) \\
\end{array}$
You fill in the reasons.
In a truth table we need $\displaystyle 2^5$ rows. WHY?