Last Friday has sure been a remarkable one. Not only, because of the storm that caused all schools and universities except ours to close, but also because last Friday has witnessed my first csc165 test. The test was not so bad (at least, not as bad as I thought it would be). You see, once the sample answers for assignment one were posted, I discovered many hidden mistakes I didn't even consider.
One main problem, that I discovered after comparing my answers to the sample answers, was that I translate literally from English to symbols without taking in consideration the ambiguity in English wording which might require extra quantifiers to disambiguate.
Here is a concrete example:
S1: There is one developer more important than code finger
my answer (which is not quite right) was:
∃x ∈X, ∃y∈X, I(x, Codefinger) ∧ I(y, Codefinger) ⇒ E(x,y)
What this is saying is:
if you pick two developers who are more important than Code finger, they will be the same person. Which is fine, except it doesn't quite say the same thing as S1.
I had this problem of not being able to precisely translate English into symbols until I decided to use the friend-enemy game we used in defining limits.
Here is what S1 mean unambiguously:
If you pick a developer who is more important than code finger then any developer you pick after that if he is more important than Code finger, I guarantee you that he will be the same person you originally picked.
I know it might not seam as a huge change from the first explanation but it actually is: interpreting it this way means that you will introduce an existential quantifier then a universal quantifier instead of having two existential quantifiers.
This technique really helped me to determine when to introduce quantifiers.