1. 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

2. Originally Posted by fueL
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 $\displaystyle S \Rightarrow \neg G\; \vee \,G \Rightarrow \neg S$?