Week 4 SLOG - Galex Wong

Week 4 SLOG:

This weeks lecture focused primarily on the Bi implications, transitivity, mix quantifiers and proofs. I found the first hour of the lecture very challenging as it required us to try show equivalence of different implications. I found it difficult initially as I was not very familiar with laws such as De Morgan law and proving bi implications required us to be able to perform boolian algebra. I overcame this by drawing a truth table for each case and slowly noticing a pattern for performing boolian algebra. For instance, P implies Q can be expressed as not P and Q. The next part of the lecture talked about transitivity. Since I have noticed how to rearrange boolian expressions, this part of the lecture became fairly easy. These concepts were something new I learnt this week.

The next part of the lecture showed me how important the order of quantifiers are in a statement. The examples "For every woman, there is a man who is her soul mate" and "There is a man, every woman is his soul mate" aided me to understand the difference between placing existential quantifier first and universal quantifier first. After these examples, professor Zhang presented a more mathematical example which I learnt in MAT137, the formal definition of limit. By going through mix quantifiers, I realized this helped me to understand the idea of limit even better since our lecture used graphical representations. Hence I found this lecture very helpful for my studies of math as well.

The final hour of the lecture focused on writing proofs. While I have experience proving mathematical statements in the past from studying discrete mathematics, I still found writing proofs for computer science challenging since it is more logic based instead of arithmetically based. For instance "(P => R1) and (P => R2) is equivalent to (P => (R1 and R2))". To overcome the problem, I have followed closely to Polya's problems solving scheme, which I found really helpful. Overall, I am fairly confident about the course material this week and I hope I will be prepared for the upcoming mid term exam!