Exam Questions

Hey guys

Been working through May's exam, and was wondering something.

Question 1(ii) says "One can only win the Early Bird road race if one runs 30 km or more every week."

Do we interpret this as an "If and only if" statement? I.e. One can win the Early Bird road race if and only if one runs 30km or more every week?

Cause then I see it as Ex Ey ((Race(early bird) ^ Win(x,early bird)) -> Runs(x,y) ^ NOT LessThan(y,30))

Am I right in assuming this or am I reading too much into the sentence?

PS I don't know how to make all the symbols in the forum but I think you get the general idea.

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)… chances are that if you have an Ex(P->Q) then it is probably wrong..

Here is my take on it, but don’t take my word for it though..
1)
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)

2)
Using the term “One”, 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)

3)
Since we want to talk about Early Bird as a race, we have to identify its free variable (earlybird)
in our FOL. We don’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
Race(earlybird) ^

4)
So, we can write Race(earlybird) ^ Ax(Wins(x,earlybird) ->.........)

5)
What gets me is the part “One runs 30km or more every week”.
Does one write Ey(Runs(x,y) ^ ¬ LessThan(y,30))
or does one write Ay(Runs(x,y) -> ¬ 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 “No kilometres that one runs
every week are less than 30”.
If we look at the Existential form, we may interpret it as saying “Some kilometres that one runs
every week are not less than 30”
From these interpretations, it would seem that we have to go the Universal route, thus

6)
Race(earlybird) ^ Ax(Wins(x,earlybird) -> Ay(Runs(x,y) -> ¬ LessThan(y,30)))

Is that the correct way of translating the particular sentence from English to FOL? I don’t know…
the study guide doesn’t give enough guidance so I cannot say yes with absolute certainty

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..