Show that each of the following derivability claims holds in SD+. Prove using SD+ rules 1....
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Show that each of the following derivability claims holds in SD+. Prove using SD+ rules 1. (A V B), ~(A & C), ~BH (CD) 2. (((A V~A) & B) = B) 3. (B E (B & A)) (BDA) 4. (A E ~C), (A V ~C), BHA (((ADB) A) DA) 5. 6. ((C&~B) V (A & C)) + ((BA) & C) 7. (A = B), ~B+ ((CVA)~A) 8. (A V (B V C)), (DD ~A) + ((D & ~B) 9. (A V(B & C)) + (BD (CDA)) C) 10. (~D~E), ((D & F) (A = B)), ~(~A V B) 11. (A V B), (B V (ADC)) + ((CB) > B) 12. ((A = (C&A)) (FJ~E) = 13. (A (A= B)), (AC), (B & D) + (A & (C & (B & D))) ~B), (B V ~C), (CDA) - ~C (((ADC) & (BDC)) = ((A V B) > C)) 15. (CD), ((A V B) 14. C), (DD ~C), (A = ~B) (DVB) 16. (ADB), (A V C), ~(C&D) + ((ADB) Ɔ (B V ~D)) 17. (ADB), (CD), (~B V ~D) (~AV~C) 18. (~(~B & A) & (B = ~A)) + (B = (ADC)) 19. (A = B), ~(CB)~A 20. (~(B&~A) V~B) (BA) 21. (DV (E V F)), (FB), (C & (~B & A)), (DE) – E 22. ((BA) = (B = C)), ~((~B & ~A) & ~C) H (B) (A = C)) 23. ((ADB) V (BA)) 24. (A (AV (A & B))) 25. (~(A V B) = (CD (D & E))), (~BƆ ~D), E - ~D 26. (A V (C V B)) + (CV (A V B)) Show that each of the following derivability claims holds in SD+. Prove using SD+ rules 1. (A V B), ~(A & C), ~BH (CD) 2. (((A V~A) & B) = B) 3. (B E (B & A)) (BDA) 4. (A E ~C), (A V ~C), BHA (((ADB) A) DA) 5. 6. ((C&~B) V (A & C)) + ((BA) & C) 7. (A = B), ~B+ ((CVA)~A) 8. (A V (B V C)), (DD ~A) + ((D & ~B) 9. (A V(B & C)) + (BD (CDA)) C) 10. (~D~E), ((D & F) (A = B)), ~(~A V B) 11. (A V B), (B V (ADC)) + ((CB) > B) 12. ((A = (C&A)) (FJ~E) = 13. (A (A= B)), (AC), (B & D) + (A & (C & (B & D))) ~B), (B V ~C), (CDA) - ~C (((ADC) & (BDC)) = ((A V B) > C)) 15. (CD), ((A V B) 14. C), (DD ~C), (A = ~B) (DVB) 16. (ADB), (A V C), ~(C&D) + ((ADB) Ɔ (B V ~D)) 17. (ADB), (CD), (~B V ~D) (~AV~C) 18. (~(~B & A) & (B = ~A)) + (B = (ADC)) 19. (A = B), ~(CB)~A 20. (~(B&~A) V~B) (BA) 21. (DV (E V F)), (FB), (C & (~B & A)), (DE) – E 22. ((BA) = (B = C)), ~((~B & ~A) & ~C) H (B) (A = C)) 23. ((ADB) V (BA)) 24. (A (AV (A & B))) 25. (~(A V B) = (CD (D & E))), (~BƆ ~D), E - ~D 26. (A V (C V B)) + (CV (A V B))
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