Re: Predicate Logic

Jim Spriggs wrote:
> Ken Quirici wrote:
> >
> > Jim Spriggs wrote:
> > > 1st Semester Logic Student wrote:
> > > >
> > > > Hey Jim,
> > > >
> > > > Thanks. I need to build a few more of those and try and work them. I'm
> > > > having not much trouble when I'm trying to build a sym key with numbers
> > > > involved, lets say Positive Integers and am trying to symbolize
> > > > sentences such as, "There is no largest positive intiger" but when it
> > > > comes to story lines like the one you helped with the key is easy but
> > > > when trying to sym the sentences my brain is like, WTF mate.
> > > >
> > > > Does anyone know how to symbolize this sentence in SL? "Exactly one of
> > > > Mike, Dave and Sharon will win the prize."
> > > >
> > > > I came up with:
> > > > M: Mike wins the prize
> > > > D: Dave wins the prize
> > > > S: Sharon wins the prize
> > > >
> > > > (( ~M& ~D) -> S) v ((~S & ~D) -> M) v ((~M & ~S) -> D)
> > > >
> > > > but this looks wrong,
> > >
> > > You're right, if M, D and S are all false, it's true.
> >
> > If M, D, and S are all false then it's not true that "exactly one
> > of Mike, Dave and Sharon will win the prize", is it? That's
> > what he's trying to symbolize.
>
> What I meant was: he's right in thinking that it's wrong, and to
> demonstrate that I noted that the formula
>
> (( ~M& ~D) -> S) v ((~S & ~D) -> M) v ((~M & ~S) -> D)
>
> is true if M = D = S = false. Sorry I wasn't clear.

Ah. I had a sneaking suspicion just as I posted my reply. No problem -
thanks for the clarification.

Ken

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