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.
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.
I also have to do a truth table on this, but i'm nearly done with that.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.
Thanks in advance for all the help.
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 is really to be interpreted as "if... then" or something equivalent. "if A, then B"; this, by itself, makes no assertion on the truth or falsity of either A or B.
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.