SLOG week 5

   I do not want to spend all of my SLOG posts praising the course and the teaching, but for now, I will, because I am still enjoying it and learning well. So far, my favourite aspect of the course has been the way that it has focused--just as the course title implies--on reasoning and logic more than facts and memory. I have learned, so far, to think a certain way, and I find that the course material has overseen this exceptionally well. When I began the first assignment, I remembered much of what I had learned in class,  but I had not used it yet. The assignment forced me to go back, review, apply the concepts, and, finally, to internalize them. I was immersed in the practice of Boolean algebra and implication, and I really had to understand them to complete the assignment. Because of the assignment's forcing me to internalize the course concepts, it prepared me excellently for the test.

   My thoughts on the first test: I felt confident and comfortable with the material. After completing the first assignment, I felt totally prepared. The only real problem I had with it was that reading the Python functions and trying to follow them while under time constraints was a bit difficult, especially because I had to remember which one fit with which definition and then I had to retain that information to apply it to the next question. I basically ended up doing this by sorting it out first, then writing it down, and then quickly referencing my writing on the next page to recall the necessary function. This turned out to be a bit confusing, and I think I might have lost a mark just because I was flipping between pages and referencing the things I had scrawled next to each function without necessarily thinking it through each time. Either way, though, it was an interesting test.

   The last question was strange when I first read it. Presumably just as it was meant to, it pushed my logical intuition at first, because it called for sets P, Q, and D such that one of the following is true:

• There exists an x in D such that P if and only if Q.
• There exists an x in D such that P and Q.

   I understood the difference, but at first, I could not quite think of an example of sets that would fit. Eventually, I realized that picturing it as a Venn Diagram was really easy: if D was the universe, in the first one, the only occupied part of the diagram would be the overlap between the circles. On the second, the circles should overlap, but some other part of the diagram would have to be occupied as well. This led me to the easiest thing I could think of, which is a solution that would make P and Q  true, but such that P is not necessarily dependant on Q and vice versa. This satisfied the question, though I cannot remember exactly what I chose when writing. 

   The other way to satisfy the question, of course, would be to make the first statement true and the second false. The only way I can think of to do this is to make it true through vacuous truth: if every element in D falls under neither P nor Q, then the statement will be true and the second statement will be false.

   Taking a look at some other SLOGS, I see that there generally, people were comfortable with Test 1. http://slog-christone.blogspot.ca/ here is one (look under week 5).  This seems inevitable; though I congratulate myself for finding it easy, the fact is that it was easy because it was very much representative of what we have all learned so far, and no more than that. It did not really "stretch" our understanding of the concepts, so whoever understands the course well at this point was bound to do well.