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Math Help - How would I represent this proposition symbollically?

  1. #1
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    How would I represent this proposition symbollically?

    Let

    p: There is a hurricane.
    q: It is raining.


    Write this symbolically:

    There is a hurricane, but it is not raining.


    I know that ^ represents "and" and the upside down ^ represents or, what symbol represents "but" ? :S
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  2. #2
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    Re: How would I represent this proposition symbollically?

    Use '^' for 'but'.

    When you say 'but' you add something to your sentence; you add another clause with additional information. It's conjunction.

    Using '^' loses the natural language connotation of 'but' as something that somehow qualifies or mitigates the previous clause, but using '^' still does capture the essential truth functional role of 'but'.

    In this example:

    There is a hurricaine but it is not raining

    might be thought to have this sense:

    There is a hurricaine, and you'd usually you'd think that with a hurricaine it would be raining, but it is not raining.

    But in basic symbolic logic, we usually are willing to lose the "you'd usually think that with a hurricaine it would be raining" part in order to get to the more essential assertions: There is a hurricaine, and it is not raining.
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