Week 3 - Negations

In this week we learned many interesting new concepts of conjunction, disjunction, and most importantly negation.
Conjunction or 'and', brings two set as one, it is a way to modify qualification or implications so P,Q becomes P and Q. This also changes the truth table for P,Q because now in order for P v Q to be true, P and Q both has to be true, and if it turns out on of them is false or both of them is false then the answer for P v Q is false. Disjunction in other hand means 'or' and has a symbol of '^'. This makes the statement to be true if one of the P,Q is true.
Negation is a big part of this week's lesson. If we negate a statement says 'some P is a Q' this statement becomes 'not(some P is a Q)' and it is equal to the saying 'every P is a non-Q'. If we negate a statement 'not(every P is a Q)' then this becomes 'some P is not a Q'. Therefore we can conclude that when we negate some statement it changes the qualifier from 'for all' to 'there exist' or vice versa.
We also learned about DeMorgan's Law. This law I felt is the most commonsense concept I have learned this week. This law contains two definitions, one is (not(s1 and s2)) becomes (not(s1) or not(s2)), and second (not(s1 or s2)) becomes (not(s1) and not(s2)). This concept is very easy for me to understand because it is so commonsense and related to daily life. For example, we all know when 'apple and dog is animal' is false when either 'apple' or 'dog' is not animal, and when 'apple or orange' is animal' is false when 'apple' and 'orange' both are not animal.

Week 1 and 2- What we learned in class

In this week in class the teacher introduced to us many important concepts, like quantifiers, implications, converse and contraposition. All these concepts are completely new for me especially quantifiers, and that's where I had the most difficulty in these weeks. 

When I first see quantifiers in my math class (MAT137) I were completely confused about the concept and first I was thinking of it as a type of new variable where we assign a value to it. At the time I was sitting quite far from the board and the teacher was writing using chalks so I could see that well what he was writing. After that class as I went to CSC165 I was again introduced with this idea of quantifiers, and because I already had a wrong interpretation of the concept it really took me a while to adjust them and finally mastered the concept after I reviewed the slides from the course website after class. So basically quantifiers are a type of meaningful notations used by mathematicians to describe a function or a mathematical sentence precisely. The means of the quantifiers were pretty simple, turn 'A' symbol means 'for all', and mirrored 'E' symbol means 'there exist'. 

Implications were also pretty hard, but I felt its nothing in comparison with quantifiers. Implication are sentences written with quantifiers that produce a 'True' or 'False' answer by asking 'if' something and 'then' something. We also learned something called finding the counter example which I think its the best way to make a clear understanding for the implications. The implication is only 'False' when it satisfy the 'if' but not meet the requirement of 'then'. Basically this also means that 'if' something does not meet the requirement the first place, then the whole sentence is 'True' because there is no counter example. 

Converse are basically swapping the variable of 'if something' with 'then something'. So if the implication are 'if it is a dog then it is an animal' and converse are 'if it is an animal then it is a dog', so basically it produce an opposite version of what the implication means.

Contraposition statement is swapping the valuable and negate them at the same time making it equal to the original implication. So  if the implication are 'if it is a dog then it is an animal' and contraposition are 'if it is not a dog then it is not an animal'.