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16. Write a proof sequence for the following assertion. Justify each step. P pr 9 → -r - ⇒-q

16. Write a proof sequence for the following assertion. Justify each step. P pr 9 → -r - ⇒-q

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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 question 16 and 18

16. Write a proof sequence for the following assertion. Justify each step. P p➜r 9-r ⇒-9 17. Write a proof sequence for the following assertion. Justify each step. P→ 9 1} = 9^ Par (a^-b) ·}- -b 2 ⇒a Logic 18. Write a proof sequence for the following assertion. Justify one of the steps in your proof using the result of Example 1.8. 2 19. Write a proof sequence to establish that p p^p is a tautology. 20. Write a proof sequence to establish that p pvp is a tautology. (Hint: Use De Morgan's laws and Exercise 19.) 21. Write a proof sequence for the following assertion. Justify each step. (pq) v (p^-q) → p^-q 22. Write a proof sequence for the following assertion. Justify each step. (pvq) v (pvr) ⇒ -r → (pvq)
Transcribed Image Text:16. Write a proof sequence for the following assertion. Justify each step. P p➜r 9-r ⇒-9 17. Write a proof sequence for the following assertion. Justify each step. P→ 9 1} = 9^ Par (a^-b) ·}- -b 2 ⇒a Logic 18. Write a proof sequence for the following assertion. Justify one of the steps in your proof using the result of Example 1.8. 2 19. Write a proof sequence to establish that p p^p is a tautology. 20. Write a proof sequence to establish that p pvp is a tautology. (Hint: Use De Morgan's laws and Exercise 19.) 21. Write a proof sequence for the following assertion. Justify each step. (pq) v (p^-q) → p^-q 22. Write a proof sequence for the following assertion. Justify each step. (pvq) v (pvr) ⇒ -r → (pvq)
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