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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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