CSC165 Lecture 07 Disjunction Negation

CSC165&Lecture&Notes& && & &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&Created&by:&Lavender&Y.& th [Jan%20 ]%Lecture%07%Disjunction%&%Negation% % Review:% All)employee)make)under)75,000)and)over)100,000) Predicate:) u(x):& “employee&x&makes&under&75,000”& o(x):& “employee&x&makes&over&100,000”& !!!!!!!!!!!!!!!!!!!!!!!!!!∀!! ∈ !,[! ! ∧ !(!)]& • Truth&values&P,Q& (! ∧ !))is)true)if)and)only)if)both)P,)Q)are)true.)(false)otherwise)) & P% Q% P%=>%Q% T% T& T& T% F& F& F% T& T& F% F& T& & Employee% Gender% % Salary% A1% Male& 60,000& Betty% Female& &&& 500& Carlos% Male& 40,000& Doug% Male& 30,000& Ellen% Female& 50,000& Flo% Female& 20,000& & 7.1%Disjunction% & The&employee&is&female&or&earns&more&than&35,000& & e.g.&True&for&Flo,&Carlos,&Ellen& & e.g.&False&for&Doug& & Predicates:& & !(x):& “employee&x&is&female”& & R(x):& “employee&makes&more&than&35,000”& ! ! ∨ !(!)& • ! ∨ !& is&true&if&and&only&if&at&least&one&of&P,Q&are&true& • inclusive&or&BBB&True&when&both&properties&true& • English:&you&may&take&CSC148&or&SC150&for&credit&(exclusive,&not&both)& B ! ∧ ¬! ∨ (¬! ∧ !)& & B & Quantification,& Implication,& Conjunction& and& Disjunc&ion& give& ways& to& restrict& domains& under& consideration.& & & CSC165&Lecture&Notes& && & &&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&& &&&&&&&&&&&&&&& Created&by:&Lavender&Y.& • Every&D&that&is&a&P&is&also&a&Q& & ∀!! ∈ !,[! ! => !(!)]& & D& & & & & & && P&& & & Q& & & & & (empty)& &