Week 6

And now for the fun part. From doing proof structures, now we begin the actually proofs themselves.

So far this week, the professor has showed us the basic ideas of how to prove a certain proof. The proofs themselves really are just a bunch of algebraic manipulations to make the antecedent and consequent the same; which seems relatively easy for now. Some of the other things we started was using the contrapositive to prove a claim because it simplifies proving the claim as opposed to using direct proof (solving the proof as it is on the question). We also started slightly on the proof structures for the existential. Like the universal proofs, the structure is rather very simple to follow and as for the proofs for the existential, we get to set variable(s) -- which shows that it is in domain -- then substitute that variable into the claim and show that claim is true.

Some of the proof stuff is rather strange, because we need to define certain words when proving a claim. For example, in certain proof it is necessary to show that the definition of an odd number is n = 2k + 1. But as for the proofs so far, they seem a little bit understandable but I'm not so confident in my abilities to solve them.