SLOG week 7

   One of the challenging parts of the proof unit so far has been that much of the technique seems jarringly obvious when it is explained, yet in practice it seems like it would be quite obscure and very easy to fail to see. Obviously, I will have to explain this thought a bit...
   In a recent lecture, Danny went over several "proof techniques" including direct proof, indirect proof, inference rules, existential instantiation, disjunction elimination, implication elimination, universal elimination, etc. These, the way he put it, are very obvious. Universal elimination means that if you know every element of a set has a certain property, then you know that a certain given element of that set also has that property. This is the kind of thing that seems to go without saying. Indirect proof is the practice of assuming the negation of the consequent and deriving the negation of the antecedent. These concepts, as well as many others that we have learned, seem very obvious when simply written out.
   The problem comes with the application of these concepts. So far, with the proofs I have encountered, I basically go right for the direct proof and hope it works. If I can't get it to work on the first try, I go back to the "scratch work" and then hope to try again. At this point, I lack the confidence to know that certain situations calls for other proof techniques. It is almost as if they seem so obvious and intuitive to me that I do not know what really sets them apart from each other, and how they are appropriate for certain unique circumstances and not for others. I think I have only done one or two indirect proofs in class/tutorial, and when I did, it was because I had been told by the instructor/TA that indirect proofs were necessary for the given question. In a test or exam, I am not so sure that I would be able to clearly tell that indirect proof or any other sort of technique that is not a simple direct proof is necessary. I also would have a hard time discerning between all of these techniques and knowing exactly which one I was using, and I do not know whether or not that is entirely necessary or not.