To Thine Own Proof Be True - Week 4

This is the first week of proofs and thus it is the commencement of what I believe to be the scariest material I am going to learn at university. However, although I am extremely hesitant to start working on proofs, the one thing that has resonated the most with me this week is how we were taught to approach a proof. In order to do a proof, you must have an understanding about what is actually going on. It takes creativity and examples to sometimes gain this understanding. I am also realizing more and more that is also about allowing trial and error. While this is applicable to more complex proofs, the same method can be applied to simple proofs. Take this example:

P Þ (Q Þ (R Þ S))       Û        P Ù Q Ù  R Þ S

P Þ (Q Þ (ØR Ú S))   #implication

P Þ (ØQ Ú (ØR Ú S))  #implication 

ØP Ú(ØQ Ú (ØR Ú S))  #implication

(ØP Ú ØQ Ú ØR )Ú S   #associative

Ø(P Ù Q Ù R )Ú S   #DeMorgan’s Laws

P Ù Q Ù  R Þ S    #implication

Again, while the proof is simple, I still had to look at where I was starting from, figure out where I was going and understand the small steps that got me from one end to the other. I plan to use the same thought process in more complex proofs. While it may take more time, more creativity and a greater acceptance of the mistakes that I will surely make, I just have to remember: to be true to my proof, I have to start to trust in my logic.