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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50969b9e-0557-47b3-9c06-ed63c28b991b%2F751e0b4e-b632-46cb-9795-327351b4bc40%2Fhwvqem_processed.jpeg&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50969b9e-0557-47b3-9c06-ed63c28b991b%2F751e0b4e-b632-46cb-9795-327351b4bc40%2Fcdrd48t_processed.jpeg&w=3840&q=75)
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
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)