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.