# Math Help - Formal proof/truth table

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.
Post a related question and we can help you with it.

-Dan

3. Originally Posted by topsquark
Post a related question and we can help you with it.

-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:
$\begin{array}{l}
\sim J \to C \\
J \to R \\
R \to D(R) \\
\underline {D(R) \to D(J)} \\
\sim C \to \left( {D(R)D(J)} \right) \\
\end{array}$

Proof
$\begin{array}{l}
\sim C \to J\quad (1) \\
\sim C \to R \\
\sim C \to D(R) \\
\sim C \to D(J) \\
C \vee D(R) \\
C \vee D(J) \\
\left( {C \vee D(R)} \right) \wedge \left( {C \vee D(J)} \right) \\
\underline {C \vee \left( {D(R) \wedge D(J)} \right)} \\
\sim C \to \left( {D(R) \wedge D(J)} \right) \\
\end{array}$

You fill in the reasons.

In a truth table we need $2^5$ rows. WHY?