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Math Help - Modus Ponens

  1. #1
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    Modus Ponens

    Hi

    Here we go, we are told the first two propositions are true. We're asked is it valid and if so give a deduction by modus ponens and proof by contradiction.

    (i)
    We know that:
    If the equation is quadratic, then Dave can solve it;
    Dave cannot solve the equation f(x)=0.
    We conclude that:
    The equation f(x) = 0 is not quadratic.

    (ii)
    We know that:
    If the equation is quadratic, then Dave can solve it;
    Dave can solve the equation f(x)=0.
    We conclude that:
    The equation f(x) = 0 is quadratic.


    This is probably really simple but I just keep going around in circles, can anyone explain?

    Thanks
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  2. #2
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    Quote Originally Posted by bobred View Post
    We're asked is it valid and if so give a deduction by modus ponens and proof by contradiction.
    (i)
    We know that:
    If the equation is quadratic, then Dave can solve it;
    Dave cannot solve the equation f(x)=0.
    We conclude that:
    The equation f(x) = 0 is not quadratic.

    (ii)
    We know that:
    If the equation is quadratic, then Dave can solve it;
    Dave can solve the equation f(x)=0.
    We conclude that:
    The equation f(x) = 0 is quadratic.
    This is not correct. You cannot make any conclusion here.
    Just what is your question?
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  3. #3
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    Hi

    Sorry for being vague, we are asked which of the two is a valid deduction.
    For the valid one give a deduction involving modus ponens and proof by contradiction. For the invalid one explain why not.

    Thanks
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  4. #4
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    Can anyone help?

    Thanks
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  5. #5
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    Quote Originally Posted by bobred View Post
    Can anyone help?
    I thought that I answered your question.
    The first is valid.
    The second is invalid. The fallacy is call affirming the consequent.
    Last edited by Plato; September 27th 2009 at 12:54 PM.
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  6. #6
    Senior Member MacstersUndead's Avatar
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    I agree with the above, but I'll add a bit more to illustrate Plato's point

    We know that:
    If the equation is quadratic, then Dave can solve it;
    Dave can solve the equation f(x)=0.
    What if f(x) is, for example, a linear equation? If Dave can solve the equation f(x) = 0, where f(x) is a linear equation, then it is (obviously) not quadratic.

    Arguement

    X implies Y
    Y
    --
    X <-- false. There could be a third cause, say, Z for Y.
    Last edited by MacstersUndead; September 27th 2009 at 01:14 PM.
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