Week 7

    So this week we did more proofs. I feel somewhat confident, more confident than last week because of the tutorial. Plus, I learned some of the inference rules in the course notes and reviewed them during the lecture slides. So far, I know that there are introduction and elimination rules. Introduction rules allow us to introduce new logic structures (essentially, building the formula). Some introduction rules are:

a) Implication intro.: If A is assumed then B follows, then A => B

b) Universal intro.: If a is assumed to be a generic element of D and P(a) is derived, then you can conclude "For all a that is an element of D, P(a)"

c) Existential intro.: If x is an element of X is shown and if P(x) is shown, then you can conclude that "There exists an x that is an element of X, P(x)"

d) Conjunction intro.: If you know A and you know B, then you can conclude A and B.

e) Disjunction intro.: If you know A then you can conclude A or B.

    On the other hand, elimination rules allow us to break sentences down (essentially, taking the formula apart). Some elimination rules are:

a) Implication elimination: If you know A => B, then A allows you to conclude B. Also, not B allows you to conclude not A. (Opposite of implication intro.)

b) Universal elimination: If you know "For all a that is an element of D, P(a)", the domain allows you to conclude P(a). (Opposite of universal intro.)

c) Existential instantiation: If you know "There exists an x that is an element of X, P(x)", then you can pick an element with that property. (Opposite of existential intro.)

d) Conjunction elimination: If you know A and B, then you can conclude A (or B) separately. (Opposite of conjunction introduction)

and so on...

    Anyways, I think the quiz went well but mostly because the question was exactly the same as an exercise question. So I think I only did well because I remembered the solution from before. But I forgot what to put as a comment for one of the sentences…

    I'm going to meet my a2 group today to start the assignment so hopefully, I learn a lot from this assignment. Hopefully we do well again, especially since these proofs are much longer and more complicated than the exercises.

Week 6 (and a bit of 5): Proofs

    So for week 6 (and a bit of 5), the class went over proofs which is something I am not comfortable with at all so far. I somewhat understand the structure of the proof such as stating all of the assumptions and the domain before proving the rest of the claim. But the biggest difficulty I have is probably understanding why the claim is true. In the course notes, it said that the first step to writing a proof is understanding why it was true. It also said it was the hardest step. When I watch the professor write proofs in class, I kind of understand but if I were to write my own, I wouldn't know where to start or if my proof made sense to someone else. I think the concept of proof by cases is fairly easy to understand (When proving, you must consider different cases in which the proof is true but then again, writing the proof on my own would be difficult), but proof by limits is um...I'll probably ask my friends about that. I'm quite glad I did not enroll in MAT137 because supposedly it is all about proofs.

    Back to last week, the term test was okay...I think the first and last part seemed good but the second question I couldn't fully answer because I never understood the "Enemy chooses…" thing. From now on, I need to make sure I understand every single thing (I suppose I learned the hard way). I'm actually concerned about passing this course because I know proofs will not be easy for me and I still have a bit of difficulty with the previous material  (although working in groups for a1 really helped and was a good way for me to start studying for the test). I wish I worked better at home; forcing myself to go to the library sucks because I like getting food whenever I want and I can wear my PJ's. No matter, I'm going to try and study twice as hard for the next test!!!