I have recently compared two philosophy texts which are very very close in material they present: A Concise Introduction to logic 12th edition by Patrick Hurley and Introduction to Logic by Irving Copi & Carl Cohen 12th edition. I have a question about the logical Equivalence Rule Material Implication which states where ever P imples Q appears one can substitute Not P or Q and vice versa. I noticed if Not P or Q is Implicated the NOT is always on the left hand side. There is no instance of Q or Not P and the rule Material Implication being applied.
My question is if I am given "Q or Not P" can I apply Material Implication as written or must I commutate "Q or Not P" to get "Not P or Q" and then use the Material Implication rule? It seems all is done to avoid using material implication with a negative disjunct on the right hand side. What is the deal with that?
In other words, Would I get false conclusions if I deduce Q or Not P as Not Q or Not P? I am correct in guessing this may be the case? I...
Using "> " for material implication, (P > Q) is equivalent to each of (~ P v Q) and (Q v ~ P). So you can deduce either of those disjunctions. I think it's just a matter of convention to favor the first of them. The reader is expected to notice the equivalence of the two disjunctions. Now, (Q v ~ P) is certainly not equivalent to (~ Q v ~ P). From Q, you can infer the first of those disjunctions but not the second. The disjunction (Q v ~ P) is equivalent to (P > Q), whereas the disjunction (~ Q v ~ P) is equivalent to (P > ~ Q) and (Q > ~ P).