Proofs Summary

We covered the basic rules for proofs and did the "penny piles" problem during lectures. The list of basic rules was kind of like a summary on Chapter 3 --- Proof. Accompanied with tutorial exercises and quizzes, it gave me a deeper and more systematic understanding on this chapter.

Basically, I divided my working on proofs into four steps: 

1. Determine whether the statement is true of false. If the statement is false, write down the negation of it.

Sometimes it's a good idea to draw a graph when the whole statement seems too abstract. And I found   this method really helpful when I was doing 1.2 and 1.3 on assignment 2.
To prove a statement is true, instead of proving itself, we choose to prove the contrapositive occasionally. To write a negation for the original statement, first we change the quantifiers, then we negate the if-then statement. Be careful when using De Morgan's law. And parentheses are always helpful.

2. Write down the assumptions.
These include universal quantifiers and the antecedent.

3.Start from the antecedent. Reach the consequent.
If we come across an existential quantifier, we will need to give specific names and then continue the proofs. As for me,  make sure to complete the whole structure for each different case in the proof.(examples are Week 6 Tut Q3 and Q4).

4. Complete the whole structure.
These include introducing the =>, quantifiers , etc.