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
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter1: Foundations
Section1.5: Visualize Fractions
Problem 421E: Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza...
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I need #11 and #13
DIRECTIONS:
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).
You will lose points if you use any of the inference rules Resolution, Contradiction, Transposition,
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