1. (difficult) I had a difficult time understanding the proof by contrapositive because it seemed like it was simply the opposite of trivial proof. In other words, the statement is always false when Q is false. I know that is not true, so seeing the truth table to prove P(x)->Q(x)---(~Q(x))->(~P(x)) was helpful.
2. (reflective) It is interesting that WOLOG only applied to the case where x and y were of opposite parity. It totally makes sense that the proofs are the same for simple proof cases where the x and y are of the same parity, etc... It will be interesting to see how complicated cases can get and still be able to use the WOLOG in the proof.
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