MATH 301 In Class Exercise #5 Rules of Inference of Type (PC)

1. Let L_NT be , the language of Number Theory. For each of the following, which are formulas in L_NT ,write .

a)

b)

c)

2. For each of the following determine if is a propositional consequence of .

a)

b)

c)

3. The following definition was left out of the list of definitions that have been handed out in class.

Definition 2.4.5. If is a finite set of L-formulas, is an L-formula, and is a propositional consequence of , then is a rule of inference of type (PC).

Which of part 2 are rules of inference of type (PC)?