Conjunctions, Disjunctions, Negations

September 23, 2014

This week’s lecture outlined conjunctions, disjunctions, and negations.

An interesting point that was brought up in class, was the conjunctions and the use of “and” in the English language. The example that was used, was

“This is a pen and a telephone”

The sets of Pen as P(x) and Telephones as T(x) do not intersect, but this sentence means an x from Pen in addition the Telephone. English is a funny language, and has many complexities that we do not think of day-to-day.

As the class progressed on to negations, the concept, although very simple, seem to conbobulate in my mind. I started to mix up negations to verifying/falsifying statements. On top of that, although the negating of English sentence is straightforward, converting it back into symbols was unintuitive. The difference of when the wedge was used versus → was very hard to distinguish, especially with little examples (beyond simple sentences).

The other topics, conjunctions, disjunctions, I thought I had understood the concepts. However, when I went to do the Tutorial questions, I quickly realized I did not understand at all. The most difficulty was when the sentence had quantifying descriptions (e.g. more than one). Similar examples were not covered in class, so I got creative and tried using the wedge, and putting restrictions on variables. However, I had no idea what I was doing, and was very unsure of my answers going into the tutorial.

At tutorial this week, I was eager to know what the answers were to these questions. When comparing my answers to a fellow classmate (I forgot to ask his name!), I realized my conditions on variables (There exists, For all, etc) were off. I must have been too focused on the meat of the sentence. That was embarrassing.

The most neat answer to me was to the following question:

1) Symbolize the sentence, if C is courses, P(x,y) = x is prerequisite for y

6. No course has more than two prerequisites

This particular question, I had no answer for. No matter how I scratched my head, I could not get a good enough answer. This utilized three variables (i.e. x, ,y, z) that represented prerequisites. The condition on these variables, was (x=y ∨ y=z ∨ z=x), so if one these were true, then there would be two prerequisites! This made me realize that symbolizing can be a very creative process

Until next time,

Maya.

Questions, questions, questions

September 16, 2014.

At the start of lecture, Larry had presented a table, where we needed to fill in with the worlds "no", "one", "example", "counter-example". The table was laid out like so:

	Universal	Existential
Verify
Falsify

Although I have a pretty good understanding of the concepts taught last class, this table was not intuative. I understood that Verify/Falsify was True/False and Universal/Existential was for All/Some. Perhaps because I had not fully settled into the CSC165 mindset, this all seemed foreign to me. I did not know where to begin. At first, the All/Some True/False was getting mixed up in my brain, but as that came more clear, allocating the words into the table was nonsensical. I had thought each of the words some how correspond to the box. So I formatted my table to look something like this:

	Universal	Existential
Verify	counter-example	example
Falsify	one	no

Of course it was entirely wrong. As soon as Larry  had done the first example, my mistakes became very apparent, and I had slapped my forehead, disappointed in my misunderstanding.

As Larry started covering "Evaluating Quantified Claims", and Python syntax were introduced, the for/in/in made it very confusing. The chattering classroom (understandable--people are eager to answer the question!) made it harder to concentrate, to clear the meaning in my head.

At this point, I was feeling down and discouraged, as it seemed to me that I could not keep up with the classroom. I made a mental note to review and practice Python more, so the syntax will be obvious and second-nature to me. This is what I am getting into! The questions were difficult, but I had still made an effort to answer, whether they were erroneous or not. These questions are very good, and got everyone thinking, so please do not misunderstand my frustrations to be negative feedback towards these questions!

The second half of the lecture got more into words/sentences and representing their meanings into symbols. I am currently taking PHL245 (as recommended by the Undergraduate office), and the concepts and questions were oddly familiar. I had already done many similar questions in the PHL course, so these questions were less of a struggle than the initial half. It was good for my confidence, as I was able to answer the questions more promptly. This is not saying there was not any questions that did not get me stumped! The English language can be very complex, and many ways to convey a particular meaning.

One tricky question was when identifying whether a sentence was a statement or not. The specific sentence was: "The sandwich tastes delicious". In my mind, “the sandwich” is a very specific item. When you’re saying this sentence, you are referring to a specific sandwich. However, as Larry later pointed out, there is no context in which the sentence is being spoken, thus losing its quantifying characteristic, not longer making it a statement. Hm!

Finally, the last challenge was to convert the sentence introduced at the beginning of the lecture into symbols. This part was very briefly skimmed over, and not enough time was allocated to work on the question. However, it was very interesting exercise, and I hope it would be done in a similar way in years to come.

---

September 18, 2014

This was the first week of tutorial, so I thought I might was well briefly review about that as well. The tutorial was brief, and little to no teaching was done. Only the exercises were taken up and quiz completed. Perhaps there was not enough content to cover, but more involved exercises, similar to what was done in class, would have been beneficial. The most confusing topic, implications, will hopefully be covered in next tutorial, with plenty of questions. Although I am taking PHL245 which covers similar topics, it would still benefit me greatly.

Until next week;

Maya.

Hello CSC165

Class: September 11, 2014

The first week of classes. Mostly introduction lectures, and CSC165 was no exception. The class is a 3 hour lecture. Half of the class was dedicated to expectations, assignments, etc. Larry had tried to make it as amusing as he could, which I think he successfully did. The class was laughing, I was laughing. All good times. 

Once the lecture started after a quick break, the first interactive part of the course was discussing the ambiguity of newspaper headlines. My initial thought was the misunderstandings (ambiguity) the article (body) can give rise to. For example, “Death may cause loneliness, feeling of isolation”. If I were to answer the question on my understanding, it would be how the article focused on a very specific group of people, or how it omitted other circumstances, etc. I felt silly when I heard other answers from other students. Whoops. An example of ambiguity and double meaning.

The next section was more problems solving and working through logic. It was very interesting, as it got me involved, trying to solve the problems, instead of a one way interaction (typical classes). However, the Street Car Drama problem, there is a conclusion that I STILL do not agree with. The problem requires you to find the age of the three kids of B. Each line from B concludes a fact about the children, that will be used to find the final answer.

A: Haven’t seen you in ages! How old are your three kids now?

B: The product of their ages (integers in years) is 36.

A: That’s doesn’t really answer my question...

B: Well the sum of their ages is -- [fire engine goes by] A: Hmm... that still doesn’t really tell me how old

they are.

B: Well, the eldest one plays piano.

A: Okay, I see, so their ages are -- [you have to get off the streetcar]

From the 4th line, the conclusion is that the sum of their ages do not produce a unique answer. If you were in that situation, however, it would not be realistic to assume that the sum is not a  unique answer. B is just telling you the sum of their ages, which can be either unique or not unique. I need to remember that this is a LOGIC question, and treat it as such. 

It was an enjoyable class. Still early to know what to expect in the future, but I’m looking forward to it!