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Math Help - Logical Argument #3...To be valid or not to be

  1. #1
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    Logical Argument #3...To be valid or not to be

    This will be the last problem for tonight, I don't want to make it appear like I am abusing anyone's help, but I am a step by step learner and this is definitely helping me grasp the concept, thanks in advance. I will try to use the information I have gathered from the first two problems and try to identify the statements more precisely.
    ---------------------

    Explicitly identify the component statements that are part of the argument and show the symbolic form of the argument.

    Decide whether the argument is valid or invalid. Here you may use truth tables, standard forms, Euler diagrams, and/or logical manipulation. If the argument is invalid, point to its logical fallacy.
    -----------------------

    "If the fossil is an ammonite, then it is from the Crestaceous period. If the fossil is not from the Mesozoic era, then it is not from the Crestaceous period. If the fossil is from the Mesozoic era, then it is at least 65 million years old. Therefore, if the fossil is an ammonite, it is at least 65 million years old." Whew.

    A - fossil is an ammonite (ammonite)
    C - the Crestaceous period (Crestaceous)
    M - the mesozoic era (Mesozoic)
    S - 65 million years old. (65 million years old)

    Here goes nothing,

    If A then C
    If ~M then ~C
    If M then S
    ---------------------
    therefore, If A then S.

    I think I got it :-D

    Still need help with a Euler though :/
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  2. #2
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    Hello, stueycal!

    Explicitly identify the component statements that are part of the argument
    and show the symbolic form of the argument.

    Decide whether the argument is valid or invalid.
    You may use truth tables, standard forms, Euler diagrams, and/or logical manipulation.
    If the argument is invalid, point to its logical fallacy.


    "If the fossil is an ammonite, then it is from the Crestaceous period.
    If the fossil is not from the Mesozoic era, then it is not from the Crestaceous period.
    If the fossil is from the Mesozoic era, then it is at least 65 million years old.
    Therefore, if the fossil is an ammonite, it is at least 65 million years old."


    A - fossil is an ammonite
    C - the Crestaceous period
    M - the mesozoic era
    S - 65 million years old

    Here goes nothing:

    . . \begin{array}{cccccc} & A & \to & C & [1] \\ & \sim\!M & \to & \sim\!C & [2] \\ & M & \to & S & [3]\\ \hline \therefore & A & \to & S & [4]\end{array}

    Here is one proof . . .

    . . \begin{array}{cccccc} & A & \to & C & [1] \\ & C & \to & M & \text{CP of [2]} \\ & M & \to & S & [3]\\ \hline \therefore & A & \to & S & \text{Syllogism}\end{array}

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