What is [Implications] ?

IMPLICATION basically is "If P then Q". P is called Antecedent or Assumption and Q is called Consequent or Conclusion. ( We can also use P=>Q to represent the relationship which is P implies Q).

When we say "If you are a Asian, then you are good at math", P represents "Asian" and Q represents "Good at math". However, it does not mean P causes Q. There are two types of implication we need to distinguish: Converse of implication and Contrapositive of implication. Converse version of the example is "If you are good at math, then you are a Asian." ( It does not have the same meaning with the original sentence) Contrapositive version of the example is "If you are not good at math, then you are not a Asian." (It means the same thing)

Then we summarize a list of "Everyday Language" for P => Q:
1. If P, (then) Q.
2. When(ever) P, (then) Q.
3. P is sufficient/enough for Q.
4. Can't have P without Q.
5. P requires Q.
6. For P to be true, Q must/need to be true/ is necessary.
7. P only if/ only when Q.
8. Not P unless/ if not Q.

When we want to falsify "P(x) => Q(x)" we just need to find an x such that P(x) is true but Q(x) is false.  If P(x) does not exist and Q(x) does not exist then it will be true.

In Equivalence, when we see "If P then Q, and if Q then P", it equals "P if and only if Q" = "P iff Q" using "<=>". Also, P implies Q, and conversely. P is true exactly when Q is true. P is necessary and sufficient for Q.

Important Note: (this is what I am confused about)

Every D that is a P is also a Q.

The common way to present it is :

less common way to present is :

Some D that is a P is also a Q.

The common way:

less common: 

The stuff we learn in CSC165 is getting confusing....BE CAREFUL!!!!!!

WHAT IS SLOG?!

I am the kind of person who hates reading and writing. The reason why I choose stats and compsci as my major is to avoid writing. When I heard that we have to write essays for a computer science course, I'm like

then I figured out it is just a blog  == you can write whatever you want and use whatever tone you want. (Plz tell me if Im wrong before marking this !!!)

I am in the 6-9 session. So far I have had two lectures and we have covered some ''weird'' (According to Larry) stuff. I will use this blog as a concept review for myself. 

At first, some basic stuff such as Universal quantifier and Existential quantifier. Universal == the whole universe == every. Existential == there exits == some. If we want to disprove ''every'' we need to find one counter-example; if we want to disprove "some" then find no example to support it. Then Venn Diagram. We have learnt a lot about Venn Diagram from math courses. The only thing which is new is that using X to represent empty and using O to represent occupied. After we leant symbols about the sets. (Just memorize these symbols so we know how to use them to represent relations). I find those stuff are really simple and easy to understand. 

Next, we learnt about Sentence and Statement. Basically statement (quantified) is a subset of sentence (open). Then some new concepts came up such as Predicates (F(x) : a boolean function returning True or False), Implication ( If P, then Q). Since implication can be very tricky sometimes. I want to write another blog to mainly talk about this topic. 

[Time to sleep ZZzzz...]