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Thread: proposition question

  1. #1
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    I am having a difficult time figuring out this proposition question. The question states this: Consider the proposition: "You are not going home unless you don't want to stay in a hotel" Write the proposition in the form "if p, then q" what I have so far is "If you don't want to stay in a hotel then you are going home" which I figure is p -> ~q, however I keep second guessing myself.. if the first part is wrong, the remaining questions will also follow unfortunately Could someone point me in the correct direction if I am wrong? Or clarify that the way I am headed is at least correct?

    or maybe it is ~p->q.. which seems to be where I went wrong
    Last edited by mr fantastic; Mar 14th 2009 at 01:19 PM. Reason: Merged posts
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  2. #2
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    Quote Originally Posted by fueL View Post
    Consider the proposition: "You are not going home unless you don't want to stay in a hotel"
    The “unless” connective is one of the most confusing just behind “only if”: Unless -- from Wolfram MathWorld.
    “A unless B” means $\displaystyle \neg B \Rightarrow A$.

    You have "not going home", $\displaystyle \neg G$, unless “don't want to stay in a hotel", $\displaystyle \neg S$.
    Does that give $\displaystyle S \Rightarrow \neg G\; \vee \,G \Rightarrow \neg S$?
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