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 am wondering why is the negation never on the right hand side but only the left hand side when Implication is used?
[Q V ~P ] equivalent to [~Q V~P] ? It seems after that Material Implication is applied and I then use "Transposition" I would end up with P --> Q (the original proposition). Any help and clarity would be appreciated. Thank you.