# Basic Truth Table help required

• Dec 10th 2010, 05:58 PM
Desir0
Basic Truth Table help required
With this information:

J ^ ( J => M ) ^ ( M => H) => M ^ H

J: I have a job
M: I have money
H: I am happy

I need to do a truth table, to show that the argument is valid. Now, I completed the truth table, however I got a mix of T's and F's, which suggests the argument is not valid - thus why i am asking on here for help.

Basically, I would really apprechiate abit of help as to which order I should complete the colomns.

Thanks ;)
• Dec 10th 2010, 06:05 PM
dwsmith
Post what you get between each operator.
• Dec 10th 2010, 06:27 PM
Desir0
Well, I can fill in the first three colomns fine (as far as I know) but from then on, im not sure which order I fill them in in.
• Dec 10th 2010, 06:29 PM
dwsmith
If you can do the last column, you should be able to do the first column and the 3. Work from left to right too.
• Dec 10th 2010, 06:36 PM
Soroban
Hello, Desir0!

We need more brackets in the statement.

Quote:

. . $\bigg[J \wedge (J \to M ) \wedge (M \to H)\bigg] \to ( M \wedge H)$

$\text{I need to do a truth table to show that the argument is valid.}$
$\text{Now I completed the truth table, however, I got a mix of T's and F's,}$
$\text{which suggests the argument is not valid.}$

$\text{I would like help as to which order I should complete the columns.}$

. . $\begin{array}{|c|c|c||c|c|c|c|c|c|c|c|c|c|c|c|c|}
J&M&H & \bigg[J & \wedge & (J & \to & M) & \wedge & (M & \to & H)\bigg] & \to & (M & \wedge & H) \\ \\[-4mm] \hline\hline
T&T&T & T&T&T&T&T&T&T&T&T &T& T&T&T \\
T&T&F & T&T&T&T&T&F&T&F&F &T& T& F&F \\
T&F&T & T&F&T&F&F&F&F&T&T &T& F&F&T \\
T&F&F & T&F&T&F&F&F&F&T&F &T& F&F&F \\
F&T&T & F&F&F&T&T&F&T&T&T &T& T&T&T \\
F&T&F & F&F&F&T&T&F&T&F&F &T& T&F&F \\
F&F&T & F&F&F&T&F&F&F&T&T &T& F&F&T \\
F&F&F & F&F&F&T&F&F&F&T&F &T& F&F&F \\ \hline\hline
&&& 1 & 10 & 2 & 8 & 3 & 11 & 4 & 9 & 5 & 13 & 6 & 12 & 7 \\ \hline
\end{array}$

• Dec 10th 2010, 06:41 PM
Desir0
Quote:

Originally Posted by dwsmith
If you can do the last column, you should be able to do the first column and the 3. Work from left to right too.

Yeah, Just did that now. Got the same results i was getting before. In the final colomn i got t,f,f,t,t,f,f,t ... which is evidently not correct :(

Quote:

Originally Posted by Soroban
Hello, Desir0!

We need more brackets in the statement.

. . $\begin{array}{|c|c|c||c|c|c|c|c|c|c|c|c|c|c|c|c|}
J&M&H & \bigg[J & \wedge & (J & \to & M) & \wedge & (M & \to & H)\bigg] & \to & (M & \wedge & H) \\ \\[-4mm] \hline\hline
T&T&T & T&T&T&T&T&T&T&T&T &T& T&T&T \\
T&T&F & T&T&T&T&T&F&T&F&F &T& T& F&F \\
T&F&T & T&F&T&F&F&F&F&T&T &T& F&F&T \\
T&F&F & T&F&T&F&F&F&F&T&F &T& F&F&F \\
F&T&T & F&F&F&T&T&F&T&T&T &T& T&T&T \\
F&T&F & F&F&F&T&T&F&T&F&F &T& T&F&F \\
F&F&T & F&F&F&T&F&F&F&T&T &T& F&F&T \\
F&F&F & F&F&F&T&F&F&F&T&F &T& F&F&F \\ \hline\hline
&&& 1 & 10 & 2 & 8 & 3 & 11 & 4 & 9 & 5 & 13 & 6 & 12 & 7 \\ \hline
\end{array}$

Wow! Looks like you've knocked it on the head! Can't thank you enough :)