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Math Help - Logic question

  1. #1
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    Logic question

    I am given the following premises and asked to derive a formal conclusion and then state the conclusion.


    1. No terriers wander among the signs of the zodiac.
    2. Nothing that does not wander among the signs of the zodiac is a comet.
    3. Nothing but a terrier has a curly tail.

    So from c. we can clearly say that if you have a curly tail, you do not wander among the signs of the zodiac. But I can not infer anything from b because...

    b says..

    -Anything that wanders among the signs of the zodiac is a comet

    -If wander, then comet
    P then Q

    a. implies ~P, but we can not imply ~q from ~p

    So is the only conclusion I can form about these premises be....

    - if you have a curly tail, you do not wander among the signs of the zodiac?

    Thanks for any help you can provide.
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  2. #2
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    Re: Logic question

    Hello, ehpoc!

    I am given the following premises and asked to derive a formal conclusion
    and then state the conclusion.

    . . (a) No terriers wander among the signs of the zodiac.
    . . (b) Nothing that does not wander among the signs of the zodiac is a comet.
    . . (c)Nothing but a terrier has a curly tail.

    (a) says: If x is a terrier, then x does not wander among the signs.
    . . . \text{terrier} \to\; \sim\text{wander}

    (b) says: If x does not wander, then x is not a comet.
    . . . \sim\text{wander}\:\to\;\sim\text{comet}

    (c) says: If x has a curly tail, then x is a terrier.
    . . . \text{tail}\:\to\;\text{terrier}


    We have: . \begin{bmatrix}(c) & \text{tail} &\to& \text{terrier} \\ (a) & \text{terrier} & \to & \sim\text{wander} \\ (b) & \sim\text{wander} &\to& \sim\text{comet} \end{bmatrix}


    By the Law of Syllogism: . \text{tail}\:\to\;\sim\text{comet}

    Therefore: if x has a curly tail, then x is not a comet.

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