Difficult- In symbols and descriptions I follow exactly what the lecture is saying. Our applied linear algebra class started out learning a little bit about contrapositives so that came back to me. However when it comes time to prove a contrapositive and the examples are in sentences, I struggle. This is weird to me because with lectures one and two it was easier to think in sentences than in symbols. I can do the contrapositive example but it took me a while.
I am wondering on a test how will I know when to use the contrapositive, are there words that signal to use it? The contrapositive example given is an "if => then" problem and an example of deductive reasoning is an "if => then" so how will I know which is way is the correct way to prove a problem? Trial and error?
Reflective- The most interesting part of the material to me is that the inverse of the implication is equal to the converse of the implication, therefore the inverse is the contrapositive of the converse. I had not learned that before when we had briefly discussed this is in linear algebra but it makes sense and connected the different parts of the lecture. Making the truth table helps to solidify for me that the implication and the contrapositive are equivalent, and that the inverse and the converse are equivalent. I think I will get this even more when I do the homework questions that go along with this.
Lisa, there isn't usually "one" way to prove something. It turns out that sometimes it is easier to prove it by contrapositive, other times by induction, and others just straightforward as written. This is what makes proof classes completely different than computations classes, but it's also exciting, especially when you can figure out proofs on your own. The idea is we just want to find the truth and prove it using whatever method works best for us. It will get easier as you practice.
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