Computer Science 2209A/B Lecture Notes - Lecture 5: Propositional Variable, Metalanguage, Deductive Reasoning

• School: Western University
• Department: Computer Science
• Course: Computer Science 2209A/B
• Professor: Lila Kari

Document Summary

If the sun is shining i will go to the beach. It is either day or night it is not night. A logical argument is sound if the conclusion logically follows from the premises. If all premises are true (i. e. the conjuction of all the premises yields true), then the conclusions must also be true. Hence, if the conjunction of the premises is a and if the conclusion is c , then a ! C must be true under all assignments: it must be a tautology. This idea is used in the table below to prove that disjunctive syllogism is sound. For the proof, one only has to establish that ((p _ q) ^ :p) ! q) is always true, which can be seen from the last column of the truth table. p. 1 (p _ q) ^ :p ((p _ q) ^ :p) ! q) Example: show that from p ^ q and p ^ q !