Please read Definitions 3.1, 3.2 and 3.3 and a) prove p (~ q p) is an axiom of our deductive system. b) prove {p} Hq V p. DEFINITION 3.1. The three axiom schema of Lp are: A1: (a (3 a)) - -> -> A2: ((a (3)) ((a3) (a y))) A3: (((-3) (-a)) (((-3) a) 3)). Replacing a, 3, and y by particular formulas of Lp in any one of the schemas A1, A2, or A3 gives an axiom of Lp. -> -> -> For example, (A (A A)) is an axiom, being an instance of axiom schema A1, but (Ag (Ao)) is not an axiom as it is not the instance of any of the schema. As had better be the case, every axiom is always true: DEFINITION 3.2 (Modus Ponens). Given the formulas and ( ), one may infer. We will usually refer to Modus Ponens by its initials, MP. Like any rule of inference worth its salt, MP preserves truth. DEFINITION 3.3. Let be a set of formulas. A deduction or proof from in Lp is a finite sequence 192...n of formulas such that for each kn, (1) k is an axiom, or (2) , or (3) there are i, j