To the world of proof

This week's lesson was about the possibility of switching ∀ with ∃ without altering the truthfulness of the statement. It was very hard for me to understand and a challenging subject!

I still don't understand the graphical explanation and the difference of switching ∀ԑ with ∃б.

I think I have to see TA to figure out the difference when they are switched. I also made first step into the "Proof  World". I learned the format of proof and how to draw the consequence from the antecedent.

Looking carefully the format of proof, I was very impressed by the extent which  the human beings are trying to reach through their logical thinking. I guess that this lesson would be the most important base for the whole course and should study intensively to make strong basis.

The process of getting to know

This week, we learned about the difference between natural language and idiom and its logic interpretation into symbols.

It was very interesting that "unless" could be exchanged into "if not" but the position should be switched for the symbolic translation.

In professor's slides,

Don't knock it unless you've tried it

= Don't knock it if not you've tried it

= If not you've tried it, then don't knock it

¬ T ⇒ ¬K ≡ K ⇒ T

In idiom parts, it was amusing fact that just the subtle difference between all and some could change the choice of  '∧'  and '⇒' in symbolic interpretation such as

Every D that is  a P is also a Q

∀x ∈ D, P(x) ⇒ Q(x)

Some D that is a P is also a Q

∃x ∈ D, P(x) ∧ Q(x)

Also, we learned about how to negate and parse a logical expression.  I think the negation is very important skill to prove counterexamples and should practice as many as I could.

The first class and strain

As soon as the first class started,  I got so nervous because I had heard many times from my friends that CSC 165 was extremely difficult and one of them dropped this course, deciding to change his major.  

I thought they were smart guys so it was a big shock to me, besides, English is not even my mother tongue.

However,  now, a week later, the class is getting interesting and I find myself enjoying the class.  Yes, it is still hard to understand, sometimes so confused but definitely catching my interest.

Through the classes, I have realised that I have heard and understood other people's words and spoken to them without any logical thinking. Also, I learned how important it is to speak accurately and understand correctly in communication of professional fields.

During the first tutorial, our group members were talking about the question (d) of exercise 1,  the question was "There is one of the three python programs that fails all three test suites". We all were confused the meaning "There is one", we discussed whether "There is only one" or" There is at least one." I heard from TA later that "There is one" normally means "There is only one."

 It is very interesting fact that I never thought about the mathematical meaning of words carefully when I communicated with other people in the discussion of a meeting even where it was a very important matter to check the mathematical meaning of it .

I hope I could improve my logical thinking and speaking skills through this course, at least, to better understand others' idea and opinion as well as exactly convey my ideas to them.