# Propositional Calculus - Atomic Sentences and Truth Tables

• December 5th 2010, 02:24 PM
Desir0
Propositional Calculus - Atomic Sentences and Truth Tables
Hey.
Having a little trouble with propositional calculus.

Basically, Im told this information:

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

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

And my task is to translate into english.

This is my attempt, however I have been told that its incorrect :( so need a little assistance.

Code:

I have a Job. If I have a job then I have money. If I have money then I am happy. Therefore I have money and I am happy.
I also have to do a truth table on this, but i'm nearly done with that.

Thanks in advance for all the help.

~Desir0
• December 5th 2010, 07:33 PM
topspin1617
You're missing some "and"s.

If I have a job, and having a job makes me money, and having money makes me happy, then I have money and am happy.
• December 6th 2010, 02:59 AM
Desir0
Quote:

Originally Posted by topspin1617
You're missing some "and"s.

If I have a job, and having a job makes me money, and having money makes me happy, then I have money and am happy.

Ahh cool, thank you :)

Are you certain thats correct, because its still kinda confusing me, i'd of thought more along these lines..

I have a job, and having a job makes me money, and having money makes me happy, therefore I have money and am happy.
• December 6th 2010, 02:21 PM
topspin1617
The way you are saying it, you are asserting the truth of the statement. A sentence like this has no truth; it is only upon assigning truth or falsity to the variables that you can say something.

That's why the symbol $\rightarrow$ is really to be interpreted as "if... then" or something equivalent. $A\rightarrow B$ "if A, then B"; this, by itself, makes no assertion on the truth or falsity of either A or B.
• December 6th 2010, 03:21 PM
hmmmm
well there is also really no need for the commas and it may help to think of $\ If\ (\mbox{(I have a job) and (having a job makes me money) and (having money makes me happy)})\ Then\ (\mbox{ I have money and am happy})$ as a stage between translating
• December 6th 2010, 03:24 PM
Desir0
Ahh right, I see.

Thank you very much :) both of ya.

SOLVED
• December 6th 2010, 03:24 PM
topspin1617
I was just typing in the usual sense of the English language, where commas are accepted... and sentences don't usually have that many parentheses.
• December 6th 2010, 03:27 PM
hmmmm
haha yeah i know i was saying it was a step between translation but it doesn't really matter it solved so its ok!
• December 7th 2010, 09:40 AM
Desir0
:)

The truth table bit i was on about too, i thought i had it cracked, but now im unsure :(

In the book, it says, show that the argument is valid. Which I presume means, that all the truth values for colomn 6 should turn out True, and on my truth table they don't :/

Here's the truth table I've done, dunno if you'll be able to understand it, but its the way i'd been taught.

I worked them out in this order, colomn 4,8,2,12,10,6.