First three weeks' contents are messing up in my head. I don't really want to clear them out and categorize them based on time because I realized that they are strongly connected.
The first Tutorial Problem Set was mainly about venn diagram. The problems were straightforward and Timo(TA) secretly implied us to draw a third circle or even fourth. I was confused: what was the point of the extra circles?
However, when Prof.Heap introduced how to rewrite an English sentence into symbolic form and the idea of implication, he drew a venn diagram with three circles! Then I realized venn diagram is also useful for dealing with statements(not just sets) and each circle represents a statement.
So I tried the sentence:
for all x in T, D(x)^P(x) => Q(x);
there are three statements D(x), P(x), Q(x). So it is going to have three circles in venn diagram with 8 areas to evaluate.
Surprisingly, when I used the new method Truth Table to evaluate the same sentence, I have the same 8 different situations to evaluate!
Basically, venn diagram and Truth Table can approach the same results and with the number of statements increased, venn diagram is better in terms of space-saving and Truth Table is more straightforward and easier to understand. But both of them really help me have better understanding!
It was supposed to be a challenge to kill some time for those who were already done. It turns out you can represent as many sets as you want in a Venn Diagram, though if it's more than 3, it becomes a lot less legible: http://www.thirdwave-websites.com/blog/Venn-diagram-4-5-6-sets.jpg
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