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Statement Reason E. (s Ab)k - (SAb)c 1. (s Ab)→k 1. 2. -k 2. ~k 3. ~ (sab) 3. 4. ~ (SAb) →c 4. 5. c 5.

Statement Reason E. (s Ab)k - (SAb)c 1. (s Ab)→k 1. 2. -k 2. ~k 3. ~ (sab) 3. 4. ~ (SAb) →c 4. 5. c 5.

Advanced Engineering Mathematics
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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Need solution of question 21 and 23,27,28,29
In-Class Exercises and Problems for Section 3.1 147 17. ~ (pvr)→s 18. k→ (l v p) ~ (a →c) s → (k^g) (r→ w) → q - (lv p) (pvr)→(a→c) (r → w) → k kng Problems For each formal proof in Problems 19–23, supply the reason that justifies each statement. 19. g →~ P Statement Reason 1. g →~ p 2. g 1. 2. ~p→n 3. -p 3. 4. ~ p→n 4. 5. n 5. Statement Reason 20. r →(pv~s) 1. ~ (pv~s) 1. 2. r → (pv~ s) 2. - (pv~s) 3. 3.~r 4. q →r 4. 5. ~9 5. Statement Reason 21. (sAb)→k 1. 1. (s Ab)→ k - (sab) →c 2. ~k 2. ~k 3. ~ (sab) 3. 4. ~ (sab)→c 4. 5. c 5.
Transcribed Image Text:In-Class Exercises and Problems for Section 3.1 147 17. ~ (pvr)→s 18. k→ (l v p) ~ (a →c) s → (k^g) (r→ w) → q - (lv p) (pvr)→(a→c) (r → w) → k kng Problems For each formal proof in Problems 19–23, supply the reason that justifies each statement. 19. g →~ P Statement Reason 1. g →~ p 2. g 1. 2. ~p→n 3. -p 3. 4. ~ p→n 4. 5. n 5. Statement Reason 20. r →(pv~s) 1. ~ (pv~s) 1. 2. r → (pv~ s) 2. - (pv~s) 3. 3.~r 4. q →r 4. 5. ~9 5. Statement Reason 21. (sAb)→k 1. 1. (s Ab)→ k - (sab) →c 2. ~k 2. ~k 3. ~ (sab) 3. 4. ~ (sab)→c 4. 5. c 5.
Formal Proofs 148 Statement Reason 22. (a→b)→~ w p→~(rvs) 1. a→b 1. 2. (a→ b) →~ w 2. 3. ~ w 3. - w→(rvs) 4. ~ w→ (r v s) 4. 5. rvs 5. 6. p (rv s) 6. 7. ~ p 7. Statement Reason 23. (s v w) →~d 1. d 1. g→(c→h) 2. (s v w) →~ d 3. ~ (s v w) 4. ~ (s v w) → g 2. d. 3. - (sv w) →g 4. 5. g 5. 6. g → (c → h) 7. c → h 6. 7. Problems 24-29 are all valid arguments. Construct a formal proof for each argument. 24. r→-S 25. ~r→s 26. p→(qvr) 27. s(pr) ~ (p→r) qvr 28. pr 29. p→r
Transcribed Image Text:Formal Proofs 148 Statement Reason 22. (a→b)→~ w p→~(rvs) 1. a→b 1. 2. (a→ b) →~ w 2. 3. ~ w 3. - w→(rvs) 4. ~ w→ (r v s) 4. 5. rvs 5. 6. p (rv s) 6. 7. ~ p 7. Statement Reason 23. (s v w) →~d 1. d 1. g→(c→h) 2. (s v w) →~ d 3. ~ (s v w) 4. ~ (s v w) → g 2. d. 3. - (sv w) →g 4. 5. g 5. 6. g → (c → h) 7. c → h 6. 7. Problems 24-29 are all valid arguments. Construct a formal proof for each argument. 24. r→-S 25. ~r→s 26. p→(qvr) 27. s(pr) ~ (p→r) qvr 28. pr 29. p→r
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