First we learned that the meaning of a statement may change when we change the sequence of universal quantifiers and existential quantifiers. For example, let C be a set of courses, r(x, y) means x is the prerequisite course for y, then the meaning of "all x in C, exist y in C, r(x, y)" is different from "exist y in C, all x in C, r(x, y)". The first statement means all courses in C has a prerequisite and the second statement means there exist a course y where all courses in C are its prerequisite.,
Then we learned how to make proofs, the professor said there are two main steps of an argument to convince audience something true or false:
1. think about why you believe true/false informal reasoning.
2. write up your reasoning in a clear(existing, funny, suspenseful) way
The proof need to follow a specific structure. In class, a structure is showed:
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