Connections btw Venn Diagram&Truth Table

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!

Immediate Impression given by the course

First week's lectures really confused me because the content was basically about high school math or even simpler. I was nervous about not being able to find the hidden insights at first until we handed in those in-class assignments and were told the most of us had done it wrong. Sometimes, we take logic and expressions for granted and never give a second thought if our expression has an another way to understand. That may cause a serious problem in the field of academic. However, although I am aware of it and being trained to express precisely, I still find it challenging as a non-native speaker. Guess I need to work harder in order to get the most out of this course.