Now that some time has past since submitting the assignment, and I've reviewed the sample solutions among other things for the midterms, I can understand many of the areas I've had a lot of trouble with before. I had some difficulty understanding the concept of implications in logic, which I'm sure reflected on how I answered the fifth part of the assignment. It made sense to me when it was written with symbols in a simple form like P ==> Q, that this means that P is a subset of Q. However, when written in English or a mix of English and math, I got lost in understanding implication in a more vague English sense. Had I thought of all those questions in the assignment as "one must be a subset of the other", then I would have had a much easier time going through them. Hopefully I've learned from those mistakes and wont repeat them.
As for the midterm, it was actually pretty good. I'm a third year student, so I'm no stranger to how a lot of term tests are here at UofT, especially for first year courses. This wasn't anything like I remembered first year course tests to be, which is perhaps just because the life science courses I was in were more interested in weeding out students, or I've just matured more since then and know how to study better. That being said, I don't think it was just easy marks, I thought it was fair and you had to actually think about the problems.
The first two sections of my test were a lot like the practice test and stuff we learned in class (the q0-q3 python functions). There were a few areas where I was actually really close to making a mistake in reading the problem (the set of P3 on my test almost got me, unless I'm wrong and it actually did). Where I know I messed up was the last question (which I do think was a lot trickier than what a lot of other test papers had for that question).
So the question was something like this:
∃d∈D| P(d) ⇔ Q(d)
∃d∈D| P(d) ∧ Q(d)
Write sets for D,P, and Q that make one of these true and the other false.
So, when I saw this question at first I had no idea how to do it and thought they were identical (I mean, they do intuitively seem to be identical). For whatever reason, I had forgotten how vacuous truth worked. My understanding now is that the first statement could be true and the second false by making both P and Q false (or a set that can't have anything in it). The logic behind that would be that False = False is true, but False and False is False (makes sense).
So, I guess a set for D,P, and Q could be something like:
D is the set of all integers
P is the set of all integers x that are greater than x + 1
Q is the set of all integers y that are greater than y + 5
So, you can't really put anything into P or Q, which makes the two sides false, but the bi-implication of it true. P and Q on the other-hand are just plain false.
As for the midterm, it was actually pretty good. I'm a third year student, so I'm no stranger to how a lot of term tests are here at UofT, especially for first year courses. This wasn't anything like I remembered first year course tests to be, which is perhaps just because the life science courses I was in were more interested in weeding out students, or I've just matured more since then and know how to study better. That being said, I don't think it was just easy marks, I thought it was fair and you had to actually think about the problems.
The first two sections of my test were a lot like the practice test and stuff we learned in class (the q0-q3 python functions). There were a few areas where I was actually really close to making a mistake in reading the problem (the set of P3 on my test almost got me, unless I'm wrong and it actually did). Where I know I messed up was the last question (which I do think was a lot trickier than what a lot of other test papers had for that question).
So the question was something like this:
∃d∈D| P(d) ⇔ Q(d)
∃d∈D| P(d) ∧ Q(d)
Write sets for D,P, and Q that make one of these true and the other false.
So, when I saw this question at first I had no idea how to do it and thought they were identical (I mean, they do intuitively seem to be identical). For whatever reason, I had forgotten how vacuous truth worked. My understanding now is that the first statement could be true and the second false by making both P and Q false (or a set that can't have anything in it). The logic behind that would be that False = False is true, but False and False is False (makes sense).
So, I guess a set for D,P, and Q could be something like:
D is the set of all integers
P is the set of all integers x that are greater than x + 1
Q is the set of all integers y that are greater than y + 5
So, you can't really put anything into P or Q, which makes the two sides false, but the bi-implication of it true. P and Q on the other-hand are just plain false.
No comments:
Post a Comment