Fourth Lecture - September 30th 2014

This week we mainly focused on proofs and implementing De Morgan's law and distributive laws to prove that one statement is equivalent to another. De Morgan's law was especially fascinating to me as an implication is proven to be equivalent to a negation and a conjunction. This law was also the main focus on the tutorial where we were asked to prove some challenging statements. Another interesting concept that we learned in class was transitivity. where when there were two implications separated by a conjunction such as (P(x) -> Q(x)) ^ (Q(x) -> R(s)), then P(x) -> R(x). The diagram to demonstrate this was extremely helpful. It showed that P is a small circle completely located in Q, and all of Q is a circle located within circle R. This made it clear that any element in P would obviously be in R (the largest circle). At the end the lecture, we did an experiment with folding paper. My group and I developed an algorithm to predict the types and number of folds within the paper with an "x" amount of folds.