For each of the following sequents, provide a proof that demonstrates their validity. 1. AB, B+C FAC 2. A-, BC, DE FA&DE&C 3. AVB, ~BVC, -DVE FA&DE&C 4. ~AVB, ~DVE F (A->B)&(DE) 5. (A+B)+((B>C)&( DE), A->-AVB FA&D-E&B 6. P>Q, Q tup 7. PHQ, Q t ~P 8. PHQ, up to 9. P&-PED 10. PQ, Q-+-P EPD 11. PVR F1~PR) 12. PVR Fl~RP) 13. P&-Qt-P>Q) 14. ~P&~Q E-(PvQ) 15. ~Pv~Q E ~(P&Q) 16. ~(PvQ) E~P 17. ~(PvQ) F~P&-Q 18. P&Q=R, SH~R, QEP>R 19. P&Q=R, SH-R, Q ES>-R 20. P&Q-R, SHR, QEP&SM 21. ~~R~_P) EP 22. ~(~R+~P) FP&-R 23. PQVR, ~(~R>_P) FP&Q 24.P>QVR, (~Q&S)v(T-~P), ~(~R~~P) FT->~P 25. P=>QVR, (~Q&S)v(T~~P), ~(~R~~P) t ~T&Q 26. E=>~(JVH), J E- ~E 27. E ++(JVH), -S, JVS E-E