1. The hardest part to understand today was logical equivalence. I'm still not entirely sure what the application of it really is. On the bright side, the theorems did make sense. I wonder if I'm confused between logical equivalence and tautology. I understand that tautology is when the statement is always true regardless of the truth value of the individual parts. Logical equivalence, from what I understand, is two statements that have the same truth value no matter what the truth statements of their individual parts. After some research on google, I've gotten closer to understanding. According to millersville.edu, two statements are considered logically equivalent if those two statements are a tautology. So, any two statements can be logically equivalent, if their truth tables are the same for every combination of truth statements of their individual parts. This is going to take some further thought and some application before it's solid.
2. I am actually pretty fascinated by all of this. Who knew this would be so interesting? Not me. Anyway. I found the most interesting thing to be the idea of biconditional statements. It's pretty excellent to have an if and only if statement, because then you don't get the question wrong if you mix up the parts. I also secretly (well, not secretly anymore) loved reading the proof of biconditional statements being logically equivalent. I'm still working on a real life application for all of this though. It looks so nice on paper...there's got to be some good way to apply it all!
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