Second week

                                           15th 

• implication 
• boolean function 

  Today, it begins with quantifiers with many exercises. It is a little bit confusing sometimes even Heap made a mistake.
  Then, we learn to use a boolean function to reveal a relationship between two sets which is more brief and familiar to python in other words computer than using mathematic symbols ∈ and ⊆ . 
  At last, Heap uses an order that his mom used to talk to him in his childhood" If you eat your vegetables, then you can have dessert" as a example to clarified that if the antecedent is false, then no matter the consequent is true or false the implication is always true. So, It is true that he could do not eat vegetables but to have dessert. This white-haired man is really cute , still looked like a innocent children. 
  This concept is a little bit difficult to understand. Heap does not make explanation because of time. I have been taught this concept in MAT137. The teacher says if the antecedent is false, there is no valid condition for us to show the consequent true or false which is called vacuous truth.I hope Heap could make a explanation in the next lecture because I hear many classmates talking about this after class.
                                   

                                     16th(Tutorial)

• Meaning of "Some"

  The TA Madina is a cute girl, who leads us to review the knowledge of set learned in Lectures. Because of preparation of the tutorial material, I found it easy to follow Madina's words. 
  Although there is no new or hard something to learn, it answers a question that always bothers me.Before the tutorial, I always thought that "some" means "At least one but not all" and the fact is "Some" just means "at least" .Hence when drawing the Venn Diagrams, I always think about one more situation than others. 
  The question bothers not only me but some other students who raise the misunderstanding in the tutorial.  I guess it derives from my primary  English education. When I learn English words, I will awkwardly and directly translate English word into my mother language. "some" in Mandarin is the meaning of "At least one but not all". Luckily, the little but can not be ignored mistake has been eliminated now.


                                      17th

• Implication, Conversee, Contrapositive
• "Natural" Language(P => Q)

  At the beginning of the lecture, we do some exercise about 'Implication information'. I can understand the meaning of an implication if it is true, but I do not really understand the question"what can you deduce about the following sets". So the first half of the lecture, I am struggling to understand the answers from Heap and other students. 

  After the lecture, I asked one of my friends for help who is also not very sure the goal of the problem. Hence, I posted it on Piazza. To my delight, an instructor makes a quick reply. By the way, the instructor also eliminates my misunderstanding of a concept that the contrapositive of a implication that has quantifiers does not need to change the quantifier from the universal one to existential one.Here is the link of my post. 

  When it comes to the "Natural" Language part, Heap lists lots of sentences expressing implication P=>Q in English ways and asks us to found the corresponding P and Q. The first several sentences are plain and direct. We could find the answers without much thinking. 

  However, the next following ones become more and more confusing to distinguish which is the antecedent P and which should be the result Q. 

  I find a trick that what we need to do is to find what leads to what. For example, a sentence' You can't stay in enrolled in CSC165 without a pulse.'.We can re-read it in our mind in our own words such that 'Without a pulse means that You can't stay in enrolled in CSC165' or "With a pulse means that You can stay in enrolled in CSC165.'So the key condition that decides that whether you can enrolled in CSC165 is that if you have pulse. 

  Hence, obviously, we conclude that 'without a pulse' is the antecedent of the result "can't stay in rolled in CSC165". Namely, 'without a pulse'is P,'can't stay in rolled in CSC165' is Q. 

  I believes that my trick is like the steps of solving a problem as mentioned before and understanding the problem is an important key of solving a problem.