Use MP, MT, DS, and HS to prove that the following arguments are valid. (1) 1. R 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) (9) 2. LD (PVO)/:. LD (RW) (5) 1. RDS 2. TOR 3. (6) 1. ~S/. ~T ~M 2. NDG 3. NvM/:. G (7) 1. DDE DDF 3. F. E 2 (8) 1. GvH 2. HVI 3. I/. G 1 ~GRAY BY ~ (10) 1. (AB) C DVA 2. 3. 4. ~A/. C (11) 1. 2. 3. 4. ~DD (ADB) AD (BDC) C (13) 1. 2. 3. 4. ~ ~ - DDA CvD/:. ~ B (12) 1. (D F) ~ 2. (LVM) VR 3. 4. ~T~(LVM) (D F) v~ T/:. R ~ (A v B) Ɔ (Bv C) (BDC) VA (BDC) (A v B) -Al.. Bv C ~ . 4) 1. (PQ) [Rv (T-S)] 2. (TvR) (P.Q) 3. 4. ~ (T.S) TVRI.. R

Use MP, MT, DS, and HS to prove that the following arguments are valid. (1) 1. R 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) (9) 2. LD (PVO)/:. LD (RW) (5) 1. RDS 2. TOR 3. (6) 1. ~S/. ~T ~M 2. NDG 3. NvM/:. G (7) 1. DDE DDF 3. F. E 2 (8) 1. GvH 2. HVI 3. I/. G 1 ~GRAY BY ~ (10) 1. (AB) C DVA 2. 3. 4. ~A/. C (11) 1. 2. 3. 4. ~DD (ADB) AD (BDC) C (13) 1. 2. 3. 4. ~ ~ - DDA CvD/:. ~ B (12) 1. (D F) ~ 2. (LVM) VR 3. 4. ~T~(LVM) (D F) v~ T/:. R ~ (A v B) Ɔ (Bv C) (BDC) VA (BDC) (A v B) -Al.. Bv C ~ . 4) 1. (PQ) [Rv (T-S)] 2. (TvR) (P.Q) 3. 4. ~ (T.S) TVRI.. R

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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