CSC 165 SLOG #2: More about logic, conjunction and disjuction (Week 3)

This week, we went over the materials in the course faster than usual. It was quite hard for me to understand the material, so I had 1 hour of review time after the lecture sessions. I first learnt about natural language again which I am very familiar with due to my practice on this topic last week.

The professor told us that when we see 'unless' in English, translating it to 'if not' will make our understanding much easier. I also learnt about idiom which was fairly easy.

I also learnt about conjunction and disjunction. One is "and" and the other is "or" These are materials that I already learnt in high school.

For A(x) and B(x) to be true, both of them have to be true. If there is any counter-example to this claim, the claim is false.

For A(x) or B(x) to be true, at least one of them has to be true. If there is no true example, then the claim is false.

I made a chart to demonstrate symbol versions for 'and' and 'or'.

	And	Or
Union Symbol	∩	∪
Logical Symbol	∧	∨

The logical symbol for 'And' is called caret and 'Or' is called reversed caret.

Both union and logical symbols are acceptable as they have the same meaning.

The professor also taught that English can be tricky for conjunction and disjunction. There are inclusive and exclusive. Inclusive means X or Y or both whereas exclusive means X or Y, but not both. This was very interesting to me as there is no inclusive and exclusive situation in Korean. When we want both X and Y, we say X and Y. But if we want X or Y, we say X or Y.

Next thing we learnt is negation symbol which is ¬. The symbol means not. I thought I am fine with the negation until I faced special negation idiom part.

The professor gave us the expression shown below. I will number that expression as 1 to be clear.

#1. ∀x⊆X, P(x) ->Q(x)

Let's call the negation of expression #1 is expression #2

#2. ∃x⊆D, P(x) ∧¬Q(x)

What I first expected for the negation of expression #2 was back to expression #1. However, the professor showed us that the negation of expression #2 is not expression #1, but new expression. Let's call that new expression #3.

#3. ∀x⊆D, ¬(P(x) ∧¬Q(x))

This surprised me quite a lot. However, as I tried solving them, I realized the reason why the negation of expression #2 is not #1, but #3. Then the negation of #3 expression is back to #1. As I learn more about logic, it is getting more confusing and interesting.

Going over truth table part was easy. However, what interested me was how 4 sets would look like in the standard Venn diagram. It would have 2^4=16 regions. However, I wasn't able to draw it properly. Drawing 2 or 3 sets is easy whereas 4 sets is so hard.

As I learn more about logic, my way of thinking and dealing with problem has been improved. I hope to expand my knowledge on logic in CSC 165.

CSC 165 SLOG #1: Report on my accomplishment

I just finished studying on how to distinguish which one is antecedent or consequent. I spent 2 hours with my friend to study this topic and tutorial #2 yesterday. Then  I spent 2 hours studying for natural language, tutorial #2 and previewed the next coming-up lecture today. Now that I have put enough effort, I feel more confident in CSC 165 course. I guess practice always improves people's skills. One thing I found is that studying with friends is an efficient study technique. Both my friend and I concentrated on studying and discussed things that we do not understand. I hope to learn more in CSC 165!

CSC 165 SLOG #1: My first SLOG for CSC 165 Fall! (Week 1 and 2)

Not only is this my first SLOG, but also this is my first time making my own blog!

I had my first tutorial yesterday which was fairly easy compared to other course. It was about Venn diagram and how we can prove whether the universal and existential claim are true or not. We also went over the meaning of  ∀ and ∃.
∀ represents for all.
∃ represents for some.

The symbols were easy as I have already learnt it during high school.

I summarized it below on how to verify universal and existential claims.

For universal claim to be true, we need to check that all the examples given are true to the claim.
For universal claim to be false, we need at least one counter-example.

For existential claim to be true, we just need at least one example that supports the claim
For existential claim to be false, we need to check that all the examples provided must be counter-examples to the claim.

Verifying universal and existential claim is very fun to me. I also took my first quiz in CSC 165 and hope to achieve high score on it.

Today, I explored the topics of implication, converse and contrapositive which were new to me. Not only that, I also learnt about expressing implication in English just like shown below.

Implication: P ---> Q
Expressing implication in English: "If    P  , then   Q   ".
Where P is antecedent and Q is consequent.

But that was when I faced my first challenge in the course.

During the lecture, I had hard time figuring out which one is antecedent and consequent for each statement. That was when I realized that this course is the most confusing. The course material itself is not that hard, but I find it very confusing. In order to overcome this challenge, I decided that I will practice on distinguishing between antecedent and consequent from natural language this week. I am aiming to master today's material by this week. To check my achievement, I am going to put another post on this Sunday to see how well I have done according to my plan. If not, I will try to find some improvement with my plan to achieve success in the course.

At the end of the course, I hope to achieve more skills in order to be a computer scientist and to explore computer science.