Took 2 hours lecture after the test is so tired but start learning proof is exciting. Especially the one given in class showed that 'it is not bad even if you left everything blank and others did well'. You are much better than this if wrote something in the test.
There are several ways of thinking about proof. I believe that in most cases it is not that easy to show something directly, therefore we have to come up with some alternative ways, such us using contrapositive, contradiction. For example, to prove P=>Q is the same as prove ~Q=>~P, because we know that the contrapositive is the same as the original statement in logic. Here is the proof of that
(~Q=>~P)=>(Q or ~P)=>(P=>Q)
Another way of proving an implication statement is by using contradiction. To use this we need to assume the negation of the statement is right, then derive some results based on these assumptions, if some of them contradict each other, it means our assumptions are wrong which is the negation of the original statement. Therefore the original statement is true.
The last part of the lecture was about proof for existence. It seems easy for me because once we can show one example then we can finish the proof.
Hope everyone get a great mark for the test.
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