Class Notes (839,315)
CSC165H1 (167)
Lecture

# CSC165 Lecture 06 More Implication and Conjunction

2 Pages
98 Views

Department
Computer Science
Course Code
CSC165H1
Professor
Tom Fairgrieve

This preview shows 80% of the first page. Sign up to view the full 2 pages of the document.
Description
CSC165&Lecture&Notes& && & &&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&& &&&&&&&&&&&&&&& Created&by:&Lavender&Y.& th [Jan%17 ]%Lecture%06%More%Implication%and%Conjunction% Review% Implication)Claims:) P&=>&Q,&for&truth&values&P,&Q& ∀!! ∈ !,! ! => !(!),& & & & & A(x),&B(x)&predicate& ∃!! ∈ !,! ! => !(!),& & & & & & & & & & & & & & & & & D&B>&domain& & & & & An)Implication)is)false)when)the)assumption)is)true,) ) & & and)conclusion)false,)otherwise)the)implication)is)true.) )& P% Q% P%=>%Q% T% T& T& T% F& F(counter& example)& F% T& T& F% F& T& & & Example#1:& ∀!! ∈ !,[ ! − 2! + 2 = 0 => (! > ! + 5)]& • Conclusion&is&always&false,&suggesting&implication&false& • Assumption&always&false& • Consider& ∀!! ∈ !, ! − 2! + 2 = 0 => ! > ! + 5 & to&be&vscuously&true,&since&there’s&no& counterexample&so&that&P(x)&is&true&and&Q(x)&is&false& & Example#2:&All&employees&earning&over&100,000&are&male.& & & ∀!! ∈ !,!"#"\$% ! > 100,000 => !!(!)& & & & All&employees&earning&over&100,000&are&female.& & ∀!! ∈ !,!"#"\$% ! > 100,000 => !!(!)& & & !&are&considered&true& & Example#3:% % Consider:& & Every&male&employee&earns&between&25,000&and&45,000& & & & ∀!! ∈ !,! ! => 25,000 !(!),% ∀!! ∈ !,! ! => !(!)%
More Less

Only 80% of the first page are available for preview. Some parts have been intentionally blurred.

Unlock Document

Unlock to view full version

Unlock Document
Me

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.