C. Proofs
Give proofs for the following sequents using only the primitive rules of proof (ampersand-elim, ampersand-intro, wedge-elim, wedge-intro, double-arrow-intro, double-arrow-elim, arrow-elim, arrow-intro, and RAA).
8. $\neg(P \lor Q), R \to P \vdash \neg R$
9. $P \to Q \vdash \neg P \lor Q$
10. $Q \& R, Q \to (P \lor S), \neg(S \& R) \vdash P$
11. $\neg(P \lor Q) \vdash P \leftrightarrow Q$
12. $\vdash (P \leftrightarrow \neg P) \to Q$
12. $(P \& Q) \lor (P \& R) \vdash P \& (Q \lor R)$