MACM 101 Lecture Notes - Lecture 6: Logical Equivalence, Fraternities And Sororities, Modus Ponens

• School: Simon Fraser University
• Department: Math & Comp Sci
• Course: MACM 101
• Professor: Steven Pearce

Document Summary

Valid deductive argument: an argument such that no matter what statements we substitute in to the premises, if the resulting premises are all true, then the conclusion is also true. However, one or more premisex can be false and still provide a valid arguement. A deductive argument is valid iff (if and only if) the premises provide conclusive proof for its conclusion: using these techniques will enable us to consider only the cases wherein all the premises are true. In some cases, the logical implication is stated without proof: many rules of inference arise in the study of logic. Modus ponens rule of detachment: symbolic form: [p ^ (p -> q)] -> q, tabular form: p p -> q. T ^ u is a valid argument, by rule of detachment (modus ponens) Law of syllogism: symbolic form: [(p -> q) ^ (q -> r)] -> (p -> r, tabular form: p -> q q -> r.