EECS 1019 Lecture Notes - Lecture 3: Modus Tollens, Modus Ponens, Hypothetical Syllogism

• School: York University
• Department: Electrical Engineering and Computer Science
• Course: EECS 1019
• Professor: John Michael Machacek

Document Summary

Chapter 1: the foundation logic + proof. We now start to study mathematical proofs. We want to start from a premise (some given information) and make a valid argument to reach a conclusion. The valid argument will use tautologies from propositional logic. If you have his phone #, then you can call . You have his phone # p q p. This is a valid argument because ((p q) p) q is a tautology. Therefore, you can call p q p q. P p q q r. Remember if p(x) is a propositional function with domain d, then p(d) is a proposition for any d d. Xp(x) e. g: let d=r (real numbers) and. Since (cid:882)2=(cid:882);(cid:4666)(cid:1853)(cid:1864)(cid:1871)(cid:1867) (cid:883)2=(cid:883)(cid:4667) we can take c=0 and conclude xp(x) e. g: Start with all students in the class know logic . If a student knows logic, then they are reasonable . George, a student in class, is reasonable: sl(s, l(george, s (l(s) r(s), l(george) r(george, r(george)