week 5 proof outline

proof outline:

1. for all x in R, P --> Q:

The method we learned in the lecture is trying to prove a statement from base case or in other words, using P to get to Q by transforming the equation or inequation. (it's like the firse step of mathmatic indaction)

2. there exist a x in R, P --> Q:

Just find a example.

3. if the sttement is hard to prove:

try to prove the contropositive.