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# Truth table help?! Watch

1. Hey.

Having some trouble with truth tables.

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 have to firstly translate into an English sentence. And secondly, have to construct a truth table.

So for the first part, I get:

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.

If im wrong, please let me know

And for the truth table, I've so far done:

However im unsure which colomns to fill out next.. :/

Any help is greatly apprechiated.
2. (Original post by desir0)
So for the first part, I get:

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 believe the convention is that => has the widest scope. (ie. it should be evaluated last) So it should be read as: (J ^ ( J => M ) ^ ( M => H)) => (M ^ H) That's different from what you have written in English.
3. Yeah, Im reading it like that but still getting the same sentence.
4. (Original post by desir0)
Yeah, Im reading it like that but still getting the same sentence.
Well, your English sentence says that you have a job. But that isn't necessarily true. The symbolic sentence is just saying: "IF something THEN something else". That doesn't place any restrictions on the truth of J.

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Updated: December 2, 2010
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