Syllogisms, contrapositives, and proof presantations

**WLOG:** 
w/o loss of generallity.

*The term is used to indicate the assumption that follows is chosen arbitrarily, narrowing the premise to a particular case, but does not affect the validity of the proof in general.*

ie, with two options, u2 in u1 or u1 in u2, dont have to do it twice can just write wlog

opposite of specificaty

proof by contrapositive: really a proof by contradiction contradiction is a superset

contradiction symbol: # rotated 45