Prove: ① introduce the R premise of ￢·q·?

② ~ r→ q ① replacement

③ ~ (p ∧ q) introduction

④ q → ~ P3 replacement

⑤ ⑤ r→⑤p2④ Hypothetical syllogism

2. Prove q, ￢P→R, P→ S, ￢ s => by inference rules; Q∧R

Proof: ① Introduction of S additional premise.

② Introduction of P → S premise

③ ￢ P1② Rejection formula

④ introducing the premise of ￢ P→ R.

⑤ r3④ Hypothetical reasoning

⑥Q premise introduction

⑦ Q ∧ R ⑤ Conjunction