Class Notes (806,696)
CSC165H1 (160)
Lecture

# CSC165 Lecture 09 Rules of Logic Equivalence.pdf

2 Pages
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School
University of Toronto St. George
Department
Computer Science
Course
CSC165H1
Professor
Tom Fairgrieve
Semester
Spring

Description
CSC165&Lecture&Notes& && & &&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&& &&&&&&&&&&&&&&& Created&by:&Lavender&Y.& th [Jan%24 %]%Lecture%09%Rules%of%Logic%Equivalences% Review:% Precedence%Rules% &Highest&& ¬!&& & & & evaluate&first& & & unary& −& & !!!!!!!!!!!!!!!!!!!!!!!!∧,∨& & & & & & & & *,&/& & &&&&&&&&&& !=>,<=>!& & & & & & & +,&B& & & Lowest&&& ∀,∃& && &e.g.& & a&+&b&*&c& & & means& && a&+&(b&*&c)& &e.g& & (Unary)&7&+&B42&*&3&=&7&+&[(B42)&*&3]& & & Example:& ∀!! ∈ ℝ,∃!! ∈ ℝ, ! < ! =>!! < !& ! & & && & Means& ∀!! ∈ ℝ,∃!! ∈ ℝ, (! < ! =>!! < !)& ! ! &&&&&&&&& And&not& ∀!! ∈ ℝ,∃!! ∈ ℝ, ! < ! => (∀!! ∈ ℝ,∃!! ∈ ℝ! < !)& & [Example#1]%Consider&P(x)&=>&(Q(x)&=>&R(x)),&what&properties&does&x&have&when&this&is&true?& & & & & D& & & & & & P& & Q& & & & & & & & & & R& & & &&&&&&&&& P(x)&=>&(Q(x)&=>&R(x))&false&for&x&in&shaded&region& & & & & & true&for&x&in&shaded&regions& & 1. In&what&regions&can&x&fall&in&to&make&P(x)&=>&(Q(x)&=>&R(x))&false& • P(x)&true,&Q(x)&=>&R(x)&false& • P(x)&true,&Q(x)&true,&R(x)&false& n 2. Venn&diagram&for&n&sets&has&2 &distinct&regions& % Truth%Table% P(x)% Q(x)% R(x)% Q(x)=>R(x)% P(x)=>(Q(x)%=>R(x))% P(x)∧Q(x)% P(x)∧Q(x)=>R(x)% T% T& T& T& T& T& T& T% T& F& F& F& T& F& T% F& T& T& T& F& TT& T% F& F& T& T& F& T&
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