I need numbers 11 and 13 to be done.For 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). 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 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

Answered: Image /qna-images/answer/3979a1e3-89ff-4fbe-ab16-1edea3830db5.jpg

he following arguments are valid. (10) 1. (AB) C 2. ~DVA 3. 4. ~DD (ADB) ~A/. C (11) 1. A Ɔ (B Ɔ C) 2. ~ C 3. ~DDA 4. Cv~D/:. ~ B (12) 1. ~ (DF) 2. (LVM) VR 3. ~T~ (L v M) 4. (D F) v~ T/:. R (A v B) Ɔ (B v C) (BC) VA (BC) (A v B) (13) 1. 2. 3. 4. Al. Bv C ~ 4) 1. (PQ) [Rv (T-S)] 2. (TvR) (P. Q)

he following arguments are valid. (10) 1. (AB) C 2. ~DVA 3. 4. ~DD (ADB) ~A/. C (11) 1. A Ɔ (B Ɔ C) 2. ~ C 3. ~DDA 4. Cv~D/:. ~ B (12) 1. ~ (DF) 2. (LVM) VR 3. ~T~ (L v M) 4. (D F) v~ T/:. R (A v B) Ɔ (B v C) (BC) VA (BC) (A v B) (13) 1. 2. 3. 4. Al. Bv C ~ 4) 1. (PQ) [Rv (T-S)] 2. (TvR) (P. Q)

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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