1. ## Formal proof/truth table

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.

2. Originally Posted by *skywalker*
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.

-Dan

3. Originally Posted by topsquark

-Dan
the attached document shows the question that this was with!!

4. 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?