A few things…
Last class we were introduced to something that we wished we all knew before the exam…
THE BIG QUESTIONS:
1) To prove something, what am I requires to do?
2) What am I allowed to use?
Since Casey shared the “BIG QUESTIONS” I thought it would be helpful to share some of my techniques to writing proofs. The best thing technique that I found useful before writing a proof is to list out what relates to the set we were given. I go as far as writing the simple definitions that we learned in the begining of the semester to help me understand the set better. Also if I am ever stuck on the problem I realize the best thing is to step away and try it again with fresh eyes, because most of the time you see something that you had not seen before.
I also wanted to discuss some of chapter 4.2…
statement: p =>q
Contrapositive: ~q => ~p
Converse: q => p
Inverse: ~p => ~q
The orginial staement and the contrapostive are equivalent.
When p => q and q =>p , we write that as p <=> q. Where the symbol <=> is represents the phrase if and only if.
I hope this was helpful!