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Math Help - Propositional Calculus - Atomic Sentences and Truth Tables

  1. #1
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    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
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by topspin1617 View Post
    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.
    Last edited by Desir0; December 6th 2010 at 04:02 AM.
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  4. #4
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    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.
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  5. #5
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    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
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  6. #6
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    Ahh right, I see.

    Thank you very much both of ya.

    SOLVED
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  7. #7
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    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.
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  8. #8
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    haha yeah i know i was saying it was a step between translation but it doesn't really matter it solved so its ok!
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  9. #9
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    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.
    Attached Thumbnails Attached Thumbnails Propositional Calculus - Atomic Sentences and Truth Tables-truthtable.png  
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