For the second picture I only need numbers #11 and #13 to be doneFor each proof, you must include (i.e., write) the premises in that proof. I do not want to see any proofs without premises. Do not use any transformation rules (e.g. contraposition) in your proof other than DN.Only use the eight inference rules. YOU CANNOT USE CONDITIONAL PROOF (CP), INDIRECT PROOF (IP), OR ASSUMED PREMISES (AP). Use MP, MT, DS, and HS to prove that the following arguments are valid.(1) 1. R2. SDR/.. ~ S-(2) 1. A S.2. (A.S) DR/.. R(3) 1. (HK)2. Rv (H.K)/:. R~(4) 1. (PvQ) (R. W)2. LD (PVO)/:. LD (RW)(5) 1. RDS2. TOR3.(6) 1.(7) 1.~M2. NDG3. Nv M/. G~S/. ~ T2DDEDDF3. F. E(8) 1. GvH2. HVI3. I/. G(9) 1 ~GRAY BY2(10) 1. (AB) CDVA2.3.4.~~A/. C(11) 1. AƆ (BƆC)2.~ C3.4.~DDACvD/:. ~ BDD (ADB)(12) 1. (DF)~2. (LVM) VR3.4.~~T~(LVM)(D F) v~ T/:. R~(13) 1.(A v B) Ɔ (Bv C)(BC) VA2.3. (BDC) (A v B)4.-Al.. Bv C.4) 1. (PQ) [Rv (T-S)]2. (TvR)(P.Q)3.4.~(T.S)TVRI.. R 1.2.3.1. Cv (~Dv-X)2. ~C3. X1. AD B2. B3. ~AD (~Cv B)1. AD D2. ~Dv (~B~~~~A)3. ~A4. ~B/~D (Note: /~D means: prove ~D)/~C/~~~~A

Answered: Image /qna-images/answer/d755a50c-0273-4979-97a7-ddca4da8b032.jpg

Use MP, MT, DS, and HS to prove that the following arguments are valid. (1) 1. R (10) 1. (ADB) C DVA 2. 3. 4. ~A/. C 2. SDR/.. ~ S (2) 1. A S * 2. (A.S) DR/.. R (3) 1. ~ (HK) 2. Rv (H.K)/:. R (4) 1. (PvQ) (R. W) 2. LD (PVO)/:. LD (RW) (5) 1. RDS 2. TDR 3. ~S/. ~T (6) 1. ~M 2. NDG 3. NvM/:. G (7) 1. DDE DDF 3. F. E 2 (11) 1. AD (BOC) 2. C 3. 4. (12) 1. ~DD (ADB) (13) 1. 2. 3. 4. ~ (D-F) 2. (LVM) VR 3. 4. 2 - DDA CvD/:. ~ B ~ ~T~(LVM) (D F) v~ T/:. R ~ . (A v B) (Bv C) (BDC) VA (BDC) (Av B) -Al.. Bv C ~ 4) 1. (PO) [Rv (T-S)] 2. (TVR) (P.Q) 3. ~ (T.S)

Use MP, MT, DS, and HS to prove that the following arguments are valid. (1) 1. R (10) 1. (ADB) C DVA 2. 3. 4. ~A/. C 2. SDR/.. ~ S (2) 1. A S * 2. (A.S) DR/.. R (3) 1. ~ (HK) 2. Rv (H.K)/:. R (4) 1. (PvQ) (R. W) 2. LD (PVO)/:. LD (RW) (5) 1. RDS 2. TDR 3. ~S/. ~T (6) 1. ~M 2. NDG 3. NvM/:. G (7) 1. DDE DDF 3. F. E 2 (11) 1. AD (BOC) 2. C 3. 4. (12) 1. ~DD (ADB) (13) 1. 2. 3. 4. ~ (D-F) 2. (LVM) VR 3. 4. 2 - DDA CvD/:. ~ B ~ ~T~(LVM) (D F) v~ T/:. R ~ . (A v B) (Bv C) (BDC) VA (BDC) (Av B) -Al.. Bv C ~ 4) 1. (PO) [Rv (T-S)] 2. (TVR) (P.Q) 3. ~ (T.S)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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