I tried to give a detailed answer, but this stupid forum keeps on giving a database error
Although you said that it sounded like it might be a biconditional, you did not actually translate it
into FOL using a biconditional but you stated ExEy (Something ->
Something else)â€¦ chances are that if you have an Ex(P->Q) then it is probably wrong..
Here is my take on it, but donâ€™t take my word for it though..
Since Running (Q) is a necessary condition for Winning (P), we must write it in the form P->Q
(P is a sufficient condition for Q but Q is a necessary condition for P, ie, winning is a sufficient
reason for running, but running is a necessary condition to win the race)
Using the term â€œOneâ€, we have to assume that the speaker is generalizing, thus talking about
something that is true of everybody (every person in the domain), thus we will have to use a
universal quantifier (Ax)
Since we want to talk about Early Bird as a race, we have to identify its free variable (earlybird)
in our FOL. We donâ€™t want to introduce it for the first time inside the scope of any of our
quantifiers, so in this case it will be best if we state Race(earlybird) first and once we have done
that, continue writing the rest of our sentence, thus we start our sentence with
So, we can write Race(earlybird) ^ Ax(Wins(x,earlybird) ->.........)
What gets me is the part â€œOne runs 30km or more every weekâ€.
Does one write Ey(Runs(x,y) ^ Â¬ LessThan(y,30))
or does one write Ay(Runs(x,y) -> Â¬ LessThan(y,30)).
Runs(x,y) already means x Runs y km every week.
If we look at the Universal form, we may interpret it as saying â€œNo kilometres that one runs
every week are less than 30â€.
If we look at the Existential form, we may interpret it as saying â€œSome kilometres that one runs
every week are not less than 30â€
From these interpretations, it would seem that we have to go the Universal route, thus
Cool, thanks Hexium. This is a tricky one, because I'd assume that because they say "ONE can only win the race..." we should not use the universal route, but I see your point.
I wish they'd give us proper examples in the study guide, because seeing these things in the exam for the first time is really silly. Half of this course is guesswork thanks to the poor study guide. I mean at least give us solutions to the textbook questions.
Although I would always welcome more, this study guide is still half acceptable to me... try those two Analysis subjects (ICT2621 and ICT2622) - I did them last semester ; no study guide, no interest from the lecturers, blotched assignments, incompetent communications from the lecturers.. the whole experience was surreal, I couldn't believe what my eyes were seeing.. Of the two, ICT2622 was the worst. I should have laid a formal complaint.. hope they fixed that big old mess. Unfortunately it's still the same lecturers so I doubt it..