Week 3

In week 3, we came to the end of the beginning stage of this course where we were actually going to dig deeper into the realm of logics. Also, this was the week when the assignment 1 was assigned. At first, I thought the assignment was going to be difficult because I had not gotten all concepts and ideas from the previous lectures; however, I was lucky that I was able to work in groups with my friend who knew the materials much better than I did. Anyway, we went through the assignment and various materials together. It was really helpful for me because not only I was working on the assignment, but I also got to review some critical terminologies and concepts. Nevertheless, we were stuck on the last question because we could not find a better way explaining either statement #1 was implied by the statement #2 or implied statement #2. It was unfortunate that we couldn't make it to the office hours to ask professor heap for a better way explaining our answers due to some private reasons, but we were still quite positive that our answers were good enough to earn full marks.

Moreover, we learned about various laws: commutative, associative, distributive, and De Morgan's law.

I knew these laws were important because I will need to know them enable to identify my steps as I went through questions that wanted me to prove either two statements were equivalent or not. 

For example: 

(P ⇒ Q) is equivalent to [(P ∧ (¬Q)) ⇒ (¬P )]

• ⇐⇒  ¬(P∧(¬Q))∨(¬P)  --> Implication 
• ⇐⇒  (¬P∨¬(¬Q))∨(¬P) -->De Morgan's 
• ⇐⇒  (¬P∨Q))∨(¬P) --> Double negation 
• ⇐⇒  (¬P ∨¬P))∨Q --> associative and commutative 
• ⇐⇒  ¬P∨Q --> idempotency
• ⇐⇒  P⇒Q --> implication