Week 7 - Prove by disprove

    During the week, the lectures on proof techniques are being summed up. Through out the few weeks I am starting to get used to the structures and techniques in proofs. They do not look as horrifying as they were few weeks ago;  I start to feel comfortable doing proofs. However, some times there is still one or two specific things that boggles my thinking. 

Up to this point, many of the proofs are well expressed and specified to be proven. However, being introduced this week, I need to start verify the claim first before I can get my hands working. 

I was introduced to disproving a claim this week. It is used when the claim is proven to be false. To work on a disprove, one need to prove the negation of the claim to be True. Since the negation of the claim is true, the claim must be false or it will no be justify in logic. Disproving works in similar structure of a proof. Therefore it was not too hard to get the hang of the work. However, verifying the proofs was the hard part since it takes certain situation to falsify the claim. Too often, its quite consuming to figure out the light bulb. During a in lecture exercise,  I was given a proof and told to fill the proof as much as possible in a short period of time. However, very few ideas popped up. It can also be quite struggling to disprove. As a result, I try to list out many of the facts that the claim provides and find the ones that did not make too much sense.

*That tutorial was a pain.