Week 3

An interesting topic we learned about this week was vacuous truths. This says that in an implication, if the antecedent is false, the implication is always true, regardless if the consequent is true or not. This was not intuitive to me and took me some time to understand. One example I thought explained it well is from Wikipedia: "For example, the statement "all cell phones in the room are turned off" may be true simply because there are no cell phones in the room. In this case, the statement "all cell phones in the room are turned on" would also be true, and vacuously so, as would the conjunction of the two: "all cell phones in the room are turned on and turned off"."

This week's tutorial exercise was much more difficult than last week's. The last questions in question 1 were especially tricky and took me a little thinking to fully understand, but the tutorial sessions definitely helped me clarify the problems I had. I had an easier time understanding question 2 after I came up with examples and checked to see if the examples worked in each direction. Thankfully, the quiz was much easier than expected, but I will have to do more practice problems like this in preparation for the midterm.

We had an interesting class on Friday. Instead of having a normal lecture, we were given an activity to do. The problem was to try and predict the sequence of ups and downs for a given number of times you fold a strip of paper in half. The problem can be solved by looking at the pattern using the first few folds. Using D for down and U for up.

Folds	Sequence
1	D
2	UDD
3	UUDDUDD
4	UUDUUDDDUUDDUDD

The formula for this sequence would be to first take the previous sequence and mirror and flip it (the sequence backwards and D's become U's and vice-versa) and then append a 'D', and then append the previous sequence to the end. This could be done using recursion and I plan to implement it in Python when I have time.

We also received the first assignment this week. I managed to finish a majority of it without much trouble. I look forward to brushing up my Latex skills in order to format this thing correctly. Thanks for reading.