(2)3. Apply a series of logical equivalences and/or rules of inference to show that rg follows from the following premises. Be sure to indicate the line mumber(s) and logical equivalence or rule of inference used in each step.

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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Discrete Math 

I was confused about how to answer these questions ( I attached them). If you could help me with them,  I really appreciated it. Thank you.

This is the one I answered and not sure if it correct

1. p → q              4. r→p  2,3 D.S Disjunctive syllogism

2. (r V s) → p 

3. ¬s                  

 .·. r → q 1,4 H.S Hypothetical Syllogism  

C.
1. p» (g v r)
2. 7
3. Therefore, p-g
d.
1. -(OA (g v r))
2. Therefore, (-p v-(g v r))
(2)3. Apply a series of logical equivalences and/or rules of inference to show that 7 -»g
follows from the following premises. Be sure to indicate the line mumber(s) and logical
equivalence or rule of inference used in each step.
1. p-+4
2. v)p
3. -3
(2) 4. Use logical equivalences and rules of inference to show that -5 A (I-a)
follows from the following premises:
1. (tV t)p
2. 5t
3. p-4
4. -t
(3) 5. Write a direct proof to show that if m is an even integer then Sm+ 3 is an odd
integer.
(3)6. Write an indirect proof to show if 3m +1 is an odd integer then m is an even
integer.
Transcribed Image Text:C. 1. p» (g v r) 2. 7 3. Therefore, p-g d. 1. -(OA (g v r)) 2. Therefore, (-p v-(g v r)) (2)3. Apply a series of logical equivalences and/or rules of inference to show that 7 -»g follows from the following premises. Be sure to indicate the line mumber(s) and logical equivalence or rule of inference used in each step. 1. p-+4 2. v)p 3. -3 (2) 4. Use logical equivalences and rules of inference to show that -5 A (I-a) follows from the following premises: 1. (tV t)p 2. 5t 3. p-4 4. -t (3) 5. Write a direct proof to show that if m is an even integer then Sm+ 3 is an odd integer. (3)6. Write an indirect proof to show if 3m +1 is an odd integer then m is an even integer.
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