This week I have learnt a bunch of new things of CSC165. I found that truth table is very useful for evaluating a complicated statement. And I found myself more skillful than before to change my expression for by-implication into the disjunction of two conjunctions.I have learnt the concept of transitivity. It should be well remembered that once the sequence of universal quantifier and existential quantifier has been changed, the meaning of the whole statement would be changed. To make us understand this clearly, the professor drew several graphs to explain this problem. By studying the graphs(such as the graph of approaching infinity) he drew, I gradually understand it. Since one factor is first chosen and another factor is chosen after we now the previous factor, it is not difficult to estimate the scale. Let us put it another way, if one is determined first, another one is going to win.By studying double quantifiers, I knew that there are at least 3 ways to claim that a certain subset of the cartesian product is non-empty. There are also 3 ways to claim that en entire catesian product has some property. In these cases, the order does not change the logic.That is the end of the first two chapters.
Then we learnt some basic knowledge about proof.It is said that a proof communicates why and how you believe something to be true. Fist you need to understand why you believe the thing is true. Then you need to write it down. We learnt it by studying the example of finding proof of universally quantified implication. A proof outline contains some argument with 'assume' and 'Then'. Moreover, the comments which was leaded by # are very important in the format of proof.
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