Copyright Zeph Grunschlag, 2001-2002.Lecture 3:Propositional Eui!alencesZeph GrunschlagL3 2"nnounce#ents$%s to&ay #o!e& to 3:30-'p#%(1 &ue ne)t *on&ayC+, -Colu#.ia +i&eo ,et/or01 is hiring /or0-stu&y ca#era operators, #ulti-#e&ia an& !i&eo strea#ing people.,o e)perience reuire&.Contact technical2c!n.colu#.ia.e&u.L3 3"gen&a3autologies Logical Eui!alencesL3 43autologies, contra&ictions, contingencies5E6:" co#poun& proposition is calle& a tautology i7 no #atter /hat truth !alues its ato#ic propositions ha!e, its o/n truth !alue is T.EG:p p-La/ o7 e)clu&e& #i&&le13he opposite to a tautology, is a co#poun& proposition thats al/ays 7alse a contradiction.EG: p p $n the other han&, a co#poun& proposition /hose truth !alue isnt constant is calle& a contingency.EG: p p L3 '3autologies an& contra&ictions3he easiest /ay to see i7 a co#poun& proposition is a tautology8contra&iction is to use a truth ta.le.3663p p33p p3663p p66p pL3 93autology e)a#ple -1.2.:.a1Part 15e#onstrate that;p -p q 1