Week 3: Negation

In the third week, we learned conjunction, disjunction and negation. At first, it was not hard to understand, because conjunction just means "and", and disjunction means "or". However, the "and" and "or" in logic is sometimes different from their meaning in daily life. When we translate English into logic language, we need to be careful about those difference.

Negation is to negate a statement. We should not only change the latter part of the sentence,  we also need to change ∀ into ∃ and vice versa.

It's new for me that the negation of P(x) => Q(x) can be P(x)⋀¬Q(x). We can understand this in English by saying the opposite of "if P is true, then Q is true" is "P is true and Q is not true". 
PS: P => Q equals to ¬P ⋁ Q, which is difficult to understand. Finally, I figured it out by using an example. If our teacher wins the lottery, then he will buy us a cake. If he doesn't win, no matter whether he buys us a cake, the implication will be true. And if he buy us a cake, no matter he wins the lottery, the implication will also be true. Only when he wins but doesn't buy the cake, the implication is false. So, the truth table is like the one on the last 20th page of the slide.

Another challenging thing for me is the distributive law. Although it's like the distributive law in multiplication [like a(b+c)=ab+ac], it might take some time to get familiar with it when using in logic.

In this student's slog this week, he/she said that the word "several" is confusing in "some courses have several prerequisites" because it can means infinite cases such as three, four, thirty and so on. At first, I have the same feeling. However, I figured it out later. What we need to write is a statement in which a course has two prerequisites. In that statement, we do not tell whether there are more prerequisites for this course, so that is exactly what "several" means. 

Since things are getting harder, hope I can hold it until December.