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Math Help - How do I know if an argument is valid or invalid?

  1. #1
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    How do I know if an argument is valid or invalid?

    I just got introduced into arguments. How do I know if a certain argument is valid or invalid?
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  2. #2
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    Re: How do I know if an argument is valid or invalid?

    Quote Originally Posted by kmjt View Post
    I just got introduced into arguments. How do I know if a certain argument is valid or invalid?
    You must be more fourth coming that.
    Give us an example of your question.
    Is validity done with truth tables in your textbook?
    Or do you have argument forms?
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  3. #3
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    Re: How do I know if an argument is valid or invalid?

    Oh i was talking in general. Heres an example, is it valid or invalid (i know answer just not sure why):

    p --> (q --> r)
    q --> (p --> r)
    ____________________
    Therefore (p or q) --> t
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    Re: How do I know if an argument is valid or invalid?

    Generally speaking, I think you need to use a proof system (you should specify which one you're using) and one or more inference rules (modus ponens is most common).

    When applied to sentential logic, a formula is valid iff it is satisfied by every interpretation. Or, put another way, it's a "tautology": a statement which must always be true regardless as to what we plug into the variables.

    For example, the statement "not A or not B implies not (A and B)", under the usual (fixed) interpretation for not, and, or, and parentheses, will always be true regardless as to what the interpretation of A and B are.

    Another example, in a more sequential fashion:

    A
    B
    therefore...
    A and B

    Note that although the above argument is valid, it will still be false if one of its premises is false. Validity refers to the correctness of the logic, not the semantic interpretation.
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  5. #5
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    Re: How do I know if an argument is valid or invalid?

    When you say t do you mean T (true)? Anything implies true, so that argument is valid no matter what the premises are. (The only time A does not imply B is when A is true, but B is false.)
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  6. #6
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    Re: How do I know if an argument is valid or invalid?

    p --> (q --> r) == ~p v (~q v r)

    q --> (p --> r) == ~q v (~p v r)
    ____________________
    Therefore (p or q) --> t == ~(p v q) v t



    (p v t) == t (Universal bound law)
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