I'm reading a book about discrete math, and am learning about the rules of inference. Here's the problem:
p = "You have access to the network."
q = "You can change your grade."
i.) p--> q is false
ii.) p is true.
The book says that it cannot be concluded whether or not you can change your grade. It seems to me that it can be it can be concluded that q is false. We know that p is true and p-->q is false; it can be concluded that q is false because p-->q is false only when p is true and q is false.
The book says these p and q are propositions, NOT predicates. Am I missing something here, or is this a mistake by the author? My only guess is that the author is miswrote that p and q are propositions, and in fact is treating p and q as predicates where
p = x has access to the network
q = x can change his grade
In which case "you" are in the domain of discourse, and there exists x1 in the domain of discourse such that p(x1)^not(q(x1)) is true. In this case, it would make sense to state that the conclusion is undecidable.