CSC165 Week3

Slog Week 3

This week I learned more about implication, symbols, negation, and also learned some new concepts such as bi-implication and transitivity. But I don’t fully understand the new things and therefore, I will need to spend some time on those things.  In the lecture, vacuous truth is an interesting idea that I seldom thought about before, and I have never thought of proving an idea in this way.

At the same time, the assignment 1 came out and I am currently working on this. By doing the assignment, I realized there are some shortcomings in my way of studying. First of all, I need to spend more time reviewing the things I learned after every lecture. Second, it is also necessary to preview before lectures. Most importantly, I think I need do some homework regularly because when I was doing the assignment, I found out that with the lack of daily practice, I don't feel very confident about my work and encountered many problems that I didn’t notice before. On the other hand, I believe that practicing problem-solving questions are really helpful for tests and it would enforce memorization a lot. Since there isn’t any homework in csc165, I guess I have to search some other study materials by myself. I hope I can figure out a way to study CSC165.

Problem Solving

    E is the set of employees, F is the set of female employees, and L is the set of employees earning less than 55,000:

         ∀ χ ∈, if F(χ), then L(χ).

If the implication is true, what can you deduce the following sets:

1.      F, the set of female employees?

2.      L, the set of employees earning less than 55,000?

3.      ¯F, the set of non-female employees?

4.      ¯L, the set of employees earning at least 55,000?

If you could add a new employee, what gender and salary combination would you pick in order to falsify the implication?

The implication says in all employees, if they are female, then they earn less than 55,000.

1.      Therefore, in the first set, we can deduce that female employees earn less than 55,000.

2.      The set of employees earning less than 55,000 must contain female employees, but also they there could be male employees.

3.      For non-female employees, they could either earn more or less than 55,000.

4.      In the set of employees earning at least 55,000, there could only be male employees or no employees because the implication concludes that female employees earn less than 55,000, and therefore, there would be no female employees in this set.

If I could add a new employee, I would add a female who earns at least 55,000 in order to falsify the implication. Since this is a universal claim, to falsify this claim, we need to find at least one counter example, which is the female employee who earns at least 55,000. She is female, but she does not earn less than 55,000, and the statement is false.

The universally-quantified implication previously could be written:

∀ χ ∈, F(χ) => L(χ).

Reverse the direction, and you can have the inverse of the original implication.

∀ χ ∈, L(χ) => F(χ).

What connection is there between the truth of an implication and its converse?

         The converse of the implication states that in all employees, if they earn less than 55,000, then they are female. By comparing the implication and its converse, it can be known that they both mean that:

         F => L  If they are female, they earn less than 55,000.

         L => F  If they earn less than 55,000, then they are female.

     F ≠> ¯L  If they are female, they do not earn at least 55,000, which means they do not earn more than 55,000.

        ¯L ≠> F  If they earn at least 55,000, then they are not female, because if they are female, then they earn less than 55,000.

     ¯F => ¯L  If they are male, they earn at least 55,000 because the employees who earn less than 55,000 are female.

         ¯L=> ¯F  If they earn at least 55,000, then they are male.

CSC165 SLOG week2

CSC165 seems to be a pretty challenging course for me. Despite the fact that I am still trying to get used to the new way of teaching in university, in the same time I realize the importance of understanding each part of the course. Therefore, I felt really frustrated when I fell behind in the lecture this week. So I spent more time after class trying to figure out the parts that I didn’t understand, it helped a little bit; but more importantly, the tutorial helped me solve the problem a lot because of the slower speed of speaking and with more details. Also, the CS Help Center is a great place to go when having problems unsolved, which I went this week, though I found that everyone has to bring their own laptop because the computers there do not work.

The idea of implication that I learned this week is interesting because it seems to connect with people’s thinking and inertial thinking, but also it is a difficult material to cover fully, which makes me feel much less confident and worry about it. In the week 2 lecture, symbols are used frequently and it took me time to think of the meaning of those symbols every time when I used it. This increases my time of understanding and solving problems and the chance to fall behind in the lecture, I hope it will get better as I use more those symbols.