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Math Help - tautology

  1. #1
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    tautology

    Hi! I have a tautology problem for 3 points in my class, but i am not even at the chapter involved. I am a day away. This is the problem:


    Is it tautology? Why or why not?
    ( p ^ q) --> (p V q)




    In particular, I as yet do not understand what the arrow represent or how the relation is made between the two statement.



    I have to have this figured out by tomorrow. Any help appreciated.
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  2. #2
    Eater of Worlds
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    This isn't something to start trying to understand the night before.

    If you have p \/ q, the only way it's false is when both are false, otherwise, true.

    If you have p /\ q, the only way it's true is when both are true, otherwise, false.

    p ---> q, the only way it's false is when the antecedent, p, is true and the consequent, q, is false.

    Start by building your truth table.

    Code:
     
    p     q    p /\ q    p \/ q     (p /\ q)--->(p \/ q)
     
    T     T
    T     F
    F     T
    F     F
    There's a start. Now finish 'er up.
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  3. #3
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    Hey thanks. Stuff happens. I really appreciate the help.I'll be back.

    I undrstand the truth tables and what you said, but what is the arrow suppose to mean.
    p q p /\ q p \/ q (p /\ q)--->(p \/ q)

    T T T F
    T F F T
    F T F T
    F F T F


    I mean I understand the rules for "and" and "or," but I do not see a relation between the statement seperated by the arrow. I don't know what the arrow means.

    By the way if the elements p and q are both false then the statement p/\ q is false right?
    Last edited by rune2402; October 19th 2007 at 06:12 PM.
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  4. #4
    Eater of Worlds
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    p--->q means p then q. The only way it is false is if p is true and q is false. Go from there. Yes, you are correct about /\. It is true only when both are true. So, if both are false, it's false.
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