PAPER FOLDING!

  During this week’s lectures, we continued our slow tread through Chapter 2: Logical Notation. We learned in Monday about negation and how to move the negation sign further into the expression. We were also introduced to truth tables, which I find much more concise and convincing than Venn Diagrams. We went through logical arithmetic and DeMorgan’s law in Wednesday’s lectures, which were mostly understandable. The part that confuses me is the distributive law. I can see it is true on the Venn Diagrams but still cannot wrap my mind around it.

  The highlight of the week came Friday when we were given an exercise in lecture to find the pattern of the creases when you fold the paper from left to right. The purpose of the exercise was to implement the “problem – solving procedures” we briefly talked about during the first week of class. 

The procedure goes like this:

1    1. Understand the problem

2    2.  Plan a solution

      3.  Carry out your plan

4    4. Review any solution you achieved

  This is almost the same as the procedures I take when I solve a problem, except that I do not always plan a solution. More often than not, I will have a vague idea of a solution in my mind and proceed with it (and improvise as I go along). That had worked for me in the past, but now as I move forward to more difficult problems, I should probably consider this new problem solving strategy…….

  On a side note, I could only fold the paper 5 times when folding it in the same direction continuously, instead of 7 times (paper folding myth).

  On another side note MythBusters folded a piece of paper more than 7 times: https://www.youtube.com/watch?v=kRAEBbotuIE

Vacuous Truth

  Almost two weeks have passed since I stepped in the first lecture of CSC165. I must admit the course is not really what I expected…… and I AM LOVING IT (so far).

  I remember in our first tutorial, our TA jokingly mentioned that there are people who would spend their time debating over logic. Sitting there, I thought to myself, “Well that sounds like something I would do!” As of today, September 18^th, we have covered topics including quantifiers, if-then statements, and converses and contrapositives. Much of the topics discussed overlaps with the syllabus of MAT137, hence sometimes the lectures feel like a review for another class. However, there are several interesting problems I encountered, one of which being the case of vacuous truth.

  At first, I found the idea of vacuous truth very abstract and absurd. How can something that is false (or unrelated) in the first place make a logical if-then statement? However, after going through some examples in my head, the concept of a vacuous truth began to make sense. If the first statement of the implication is false, the if-then statement will always be true, whether the second statement is true of false. In my own interpretation, this is because the first condition of the implication (the if…. part) is false, the implication itself will have no value, and everything implied would be possible, hence true. 

  What really shocked me was the application of this concept in our tutorial questions. In one particular case where we had to draw a Venn diagram of the false case of the statement “some programs (out of 3) pass the test”. I forgot to include a “O” in the region exclusive of the 3 programs. I realized my mistake in the tutorial. The O must be included because in the case where there are no programs all statements are true, hence the application of the concept of vacuous truth.