i know these are all correctly justified. but can you tell me why??
here are some rules that you can use
1. For each of the following, state if the step justified by the statement calculus is correctly justified. (a) 6. Vo~Q Vo~ Pontoon 7. Q Vom i odebra (!) motoroq suhom vd bra 8. o~P Q to conto and bass SC, 6,7 (b) 3. Q boli doto 8 godt 4. P-Q od gleda bo SC, 3 (c) 1. VowP+~P(t/v) browoldstatia i alt 2. P(t/v) -~oPort & gode ovo SC, 1 (d) 8. Vo( PQ). VoP VvQvitettono 9. Vo( PQ). VQ + VP 10. V (PQ) , VP4 VQ SC, 8, 9 the commutative laws associative laws ] distributive laws We give below a list of tautologous schemes. 1. P V QHQ v P 2. PA QQ A PHA B | 3, P H.QHP 4. PQR.H.Q PR 5. ( PQ) V R. P v Q V R) 6. ( PQ) A R. P A (QAR) 7. PA (Q v R).. (P AQ) v (PAR) 8. P v (QAR).. ( PQ) A (P V R) 9. P APP 10. P V PHP 11. PH~~ Potravi 12. PVP 13. PQ:-: QRPR 14. PQ.A.Q R.+ PR 15. P-Q.4, QP 16. P-Q.4.Q~P 17. P Q R :: PQ-R 18. P Q R :: PQ-R 19. PAQ R. P Q R arte] idempotent laws double negation excluded middle transitivity of implication contraposition law of exportation law of importation export-import law absorption laws 20. P V (PAQ) HP 21. P (P VQ) HP 22. P+P Q.4. P Q 23. P Q... P R.A.P QAR 24, PV Q) PAQ 25. P QPV De Morgan's laws 26. P v Q.1. P R.A.Q R. R looproof by cases 27. ~PRAR. Pola 28. ~P P. . P 29. PP P proof by 30. P 1~R~R.-. Po contradiction 31. PA ~ ~P. + P - Q 32. PQQ.. P be woman 33. PQ..~P VQ377 altro 34. PQ.4. ( PQ) blolo 35. PvQ.. ( PQ) Qadino montado como 36. PvQ..Por relations between 37. P v Q.4. ~~P~Q) and connectives on 38. PAQ.4. PV ~Q) 39. PAQ.4. ~(P ~Q) ole il soled svih 40. P. P Q.1.Q+P 1. For each of the following, state if the step justified by the statement calculus is correctly justified. (a) 6. Vo~Q Vo~ Pontoon 7. Q Vom i odebra (!) motoroq suhom vd bra 8. o~P Q to conto and bass SC, 6,7 (b) 3. Q boli doto 8 godt 4. P-Q od gleda bo SC, 3 (c) 1. VowP+~P(t/v) browoldstatia i alt 2. P(t/v) -~oPort & gode ovo SC, 1 (d) 8. Vo( PQ). VoP VvQvitettono 9. Vo( PQ). VQ + VP 10. V (PQ) , VP4 VQ SC, 8, 9 the commutative laws associative laws ] distributive laws We give below a list of tautologous schemes. 1. P V QHQ v P 2. PA QQ A PHA B | 3, P H.QHP 4. PQR.H.Q PR 5. ( PQ) V R. P v Q V R) 6. ( PQ) A R. P A (QAR) 7. PA (Q v R).. (P AQ) v (PAR) 8. P v (QAR).. ( PQ) A (P V R) 9. P APP 10. P V PHP 11. PH~~ Potravi 12. PVP 13. PQ:-: QRPR 14. PQ.A.Q R.+ PR 15. P-Q.4, QP 16. P-Q.4.Q~P 17. P Q R :: PQ-R 18. P Q R :: PQ-R 19. PAQ R. P Q R arte] idempotent laws double negation excluded middle transitivity of implication contraposition law of exportation law of importation export-import law absorption laws 20. P V (PAQ) HP 21. P (P VQ) HP 22. P+P Q.4. P Q 23. P Q... P R.A.P QAR 24, PV Q) PAQ 25. P QPV De Morgan's laws 26. P v Q.1. P R.A.Q R. R looproof by cases 27. ~PRAR. Pola 28. ~P P. . P 29. PP P proof by 30. P 1~R~R.-. Po contradiction 31. PA ~ ~P. + P - Q 32. PQQ.. P be woman 33. PQ..~P VQ377 altro 34. PQ.4. ( PQ) blolo 35. PvQ.. ( PQ) Qadino montado como 36. PvQ..Por relations between 37. P v Q.4. ~~P~Q) and connectives on 38. PAQ.4. PV ~Q) 39. PAQ.4. ~(P ~Q) ole il soled svih 40. P. P Q.1.Q+P
