Ignoring my attempt at a pun (witty or not, it is infinitely better than "pain in the assignment"), this post, as you probably have realized already, will mainly be a recap of the past week (like always) along with comments on my experience with the first assignment.
The week went by rather smoothly; the lessons on conjunction, negation, disjunction, and De Morgan's laws made sense to me. The semantics of "and," "or," and "not" are generally consistent between the fields of computer science, English, and logic -- which makes it much easier to intuitively grasp the concepts.
This week, I also went to Prof. Heap's office hours. I went prepared with a list of questions and ended up gaining a lot out of the session. I cleared up my previous confusion with the Venn diagrams (hooray!) and learned one way of expressing "uniqueness" in symbolic form. Previously, I had been thinking about how to translate something like "There is one and only one soda left in the fridge" in symbolic form. From the second tutorial, we were shown how to express statements like "There is at most x ..." and "There is at least x ...", but not "There is exactly x ..." so I reasoned intuitively that it would make sense to intersect the predicates "There is at most 1 ..." and "There is at least 1 ..." in order to achieve "There is only 1 ...". Prof Heap showed me how to write this symbolically (which turns out to be super useful for assignment 1!). The trick is to say "there is at least one x in ... " and show that if "there are two of x in ... say x1 and x2, that x1 = x2". This way, you can be sure that the solution is unique.
As for assignment 1, my partners and I finished and submitted it Saturday evening. We had been working on it for the past week sporadically, but really "seriously" began to work on it Friday night. The entire process went well; we used a Google doc to write down a preliminary draft of solutions, and then we all worked on editing and processing the final copy. This way, we were able to give each other constant feedback and work on the assignment at the same time.
Working through the assignment actually turned out to be quite fun and insightful. At first, it seemed daunting (why are there so many questions! And why is it due so soon?!), but I can say it was an experimental sort of learning process. I got to apply all that I have learned in the past few weeks about negation, conjunctions, implications, etc. and actually thoroughly and deeply understand what I was doing. It's one thing to understand the concepts given in lecture, and another to be able to apply them. Actually going through the questions solidified my understanding of the course material, and finishing the project, I felt much surer of myself than before.
Also, I got to put truth tables to good use! My partners and I were discussing whether the negation of ¬ A ⇒ B was A ^ ¬B or ¬ A^ ¬B. Since the argument was going nowhere, I decided to use a truth table to figure out which one was the correct negation; after all, the truth values never lie. With the knowledge that the negation of a statement inverts the truth values, it turns out that quite clearly that the negation of ¬ A ⇒ B is ¬ A^ ¬B.
So as you see, assignment 1 was all about experimentation; there were many instances where I arrived at an "aha!" moment after working through some of the questions, and many times where pure serendipity lead to amazing results. Working with others made the assignment more fun, and overall, it was a pretty darn good experience.
That pretty much sums up my third week. See you guys next week!
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