# Thread: Basic Truth Table help required

1. ## 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

2. Post what you get between each operator.

3. 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.

4. 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.

5. Hello, Desir0!

We need more brackets in the statement.

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

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

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

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

6. 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

Originally Posted by Soroban
Hello, Desir0!

We need more brackets in the statement.

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

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