1. Symbolic [(P - Q)A~P] + Propositional P = I'm able to control the wind. Q = I'm the Avatar. If I'm able to control the wind, I'm the Avatar. However, I'm not able to control the wind. Therefore, I'm not the Avatar. ~P ~Q P - Q [(P → Q) A~P] [[P → Q) ^ ~P] → ~Q T F F F F F F F F F F F T T 2. Symbolic [(P- Q)A~Q] → ~P Propositional P = I'm able to control the wind. Q = I'm the Avatar. If I'm able to control the wind, I'm the Avatar. However, I'm not the Avatar. Therefore, I'm not able to control the wind. ~P P - Q [(P - Q) A~Q]] [P - Q) A~Q] - ~P T F F F F T F F T F T F F T. 3. Symbolic [(A A0)A~O] - A Propositional A = Peter will deliver apples on Monday. 0 = Peter will deliver oranges on Tuesday. Peter will deliver apples on Monday and oranges on Tuesday. He said he won't deliver oranges this Tuesday. Therefore, he will deliver apples on Monday. A NO (AAO) [(AA0)A0] [(A A0) AN0]→ A F F T F F F T F F T F F 4. Symbolic [(A V0)ANo] - A Propositional A = Peter will deliver apples on Monday. O = Peter will deliver oranges on Tuesday. Peter will deliver apples on Monday or oranges on Tuesday. He said he won't deliver oranges this Tuesday. Therefore, he will deliver apples on Monday. ~A (AVO) [(A V0)A~O] [(AVo)A~0]→ A T F T F F F T F F F F F 5. Symbolic [(M - G)AG] → M Propositional M = Ill deal with the module for an hour. G = Il play Genshin after the module. If Ill deal with the module for an hour, Il play Genshin after. I played Genshin after the module. Therefore, I've dealt with the module for an hour. M G M - G [(M - G) AG] [(M - G)AG]→ M T. F F F F F F F F
1. Symbolic [(P - Q)A~P] + Propositional P = I'm able to control the wind. Q = I'm the Avatar. If I'm able to control the wind, I'm the Avatar. However, I'm not able to control the wind. Therefore, I'm not the Avatar. ~P ~Q P - Q [(P → Q) A~P] [[P → Q) ^ ~P] → ~Q T F F F F F F F F F F F T T 2. Symbolic [(P- Q)A~Q] → ~P Propositional P = I'm able to control the wind. Q = I'm the Avatar. If I'm able to control the wind, I'm the Avatar. However, I'm not the Avatar. Therefore, I'm not able to control the wind. ~P P - Q [(P - Q) A~Q]] [P - Q) A~Q] - ~P T F F F F T F F T F T F F T. 3. Symbolic [(A A0)A~O] - A Propositional A = Peter will deliver apples on Monday. 0 = Peter will deliver oranges on Tuesday. Peter will deliver apples on Monday and oranges on Tuesday. He said he won't deliver oranges this Tuesday. Therefore, he will deliver apples on Monday. A NO (AAO) [(AA0)A0] [(A A0) AN0]→ A F F T F F F T F F T F F 4. Symbolic [(A V0)ANo] - A Propositional A = Peter will deliver apples on Monday. O = Peter will deliver oranges on Tuesday. Peter will deliver apples on Monday or oranges on Tuesday. He said he won't deliver oranges this Tuesday. Therefore, he will deliver apples on Monday. ~A (AVO) [(A V0)A~O] [(AVo)A~0]→ A T F T F F F T F F F F F 5. Symbolic [(M - G)AG] → M Propositional M = Ill deal with the module for an hour. G = Il play Genshin after the module. If Ill deal with the module for an hour, Il play Genshin after. I played Genshin after the module. Therefore, I've dealt with the module for an hour. M G M - G [(M - G) AG] [(M - G)AG]→ M T. F F F F F F F F
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
State your observations with the identified rules of inference. In addition, determine the significance of the observed truth tables. (at least 5 sentences)
![1.
Symbolic
[(P - Q)A~P] -
Propositional
P = I'm able to control the wind.
Q = I'm the Avatar.
If I'm able to control the wind, I'm the Avatar. However, I'm not able to
control the wind. Therefore, I'm not the Avatar.
P -Q
[(P - Q)A~P] [[P - Q) A~P] Q
F
F
F
T
F
F
F
F
F
F
T
F
T
F
T
T
T
2.
Symbolic
[(P - Q) A~Q] → P
Propositional
P = I'm able to control the wind.
Q = I'm the Avatar.
If I'm able to control the wind, I'm the Avatar. However, I'm not the Avatar.
Therefore, I'm not able to control the wind.
P
P - Q
[(P - Q) ANQ]
[(P - Q) A NQ] → ~P
F
T
F
T
T
F
F
F
T
F
F
T
T
3.
Symbolic
[(A A0)ANo] A
Propositional
A = Peter will deliver apples on Monday.
0O = Peter will deliver oranges on Tuesday.
Peter will deliver apples on Monday and oranges on Tuesday. He said he
won't deliver oranges this Tuesday. Therefore, he will deliver apples on
Monday.
(AAO)
[(A A0)A 0]
[(A A0) A~0] - A
А
T
F
F
F
F
T
F
F
F
T.
F
F
F
F
4.
Symbolic
[(A Vo)A~o] - A
Propositional
A = Peter will deliver apples on Monday.
0 = Peter will deliver oranges on Tuesday.
Peter will deliver apples on Monday or oranges on Tuesday. He said he won't
deliver oranges this Tuesday. Therefore, he will deliver apples on Monday.
A
~A
~O
(AVO)
[(AV0)A~0]
[(A Vo)A~0] A
T
T.
F
T
F
F
T
T.
F
F
F
F
F
T.
5.
Symbolic
[(M - G)AG] → M
Ртopоsitional
M = I'll deal with the module for an hour.
G = Il play Genshin after the module.
If Ill deal with the module for an hour, I'll play Genshin after. I played
Genshin after the module. Therefore, I've dealt with the module for an hour.
M
G
M - G
[(м — G) л G]
[(M - G)A G] - M
T
T
F
F
F
T
F
F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefb451c4-8845-441b-ac14-0f048c0bdadf%2Ff83f802d-3978-4397-a6e0-1ccd654e8646%2Fqjw9f2j_processed.png&w=3840&q=75)
Transcribed Image Text:1.
Symbolic
[(P - Q)A~P] -
Propositional
P = I'm able to control the wind.
Q = I'm the Avatar.
If I'm able to control the wind, I'm the Avatar. However, I'm not able to
control the wind. Therefore, I'm not the Avatar.
P -Q
[(P - Q)A~P] [[P - Q) A~P] Q
F
F
F
T
F
F
F
F
F
F
T
F
T
F
T
T
T
2.
Symbolic
[(P - Q) A~Q] → P
Propositional
P = I'm able to control the wind.
Q = I'm the Avatar.
If I'm able to control the wind, I'm the Avatar. However, I'm not the Avatar.
Therefore, I'm not able to control the wind.
P
P - Q
[(P - Q) ANQ]
[(P - Q) A NQ] → ~P
F
T
F
T
T
F
F
F
T
F
F
T
T
3.
Symbolic
[(A A0)ANo] A
Propositional
A = Peter will deliver apples on Monday.
0O = Peter will deliver oranges on Tuesday.
Peter will deliver apples on Monday and oranges on Tuesday. He said he
won't deliver oranges this Tuesday. Therefore, he will deliver apples on
Monday.
(AAO)
[(A A0)A 0]
[(A A0) A~0] - A
А
T
F
F
F
F
T
F
F
F
T.
F
F
F
F
4.
Symbolic
[(A Vo)A~o] - A
Propositional
A = Peter will deliver apples on Monday.
0 = Peter will deliver oranges on Tuesday.
Peter will deliver apples on Monday or oranges on Tuesday. He said he won't
deliver oranges this Tuesday. Therefore, he will deliver apples on Monday.
A
~A
~O
(AVO)
[(AV0)A~0]
[(A Vo)A~0] A
T
T.
F
T
F
F
T
T.
F
F
F
F
F
T.
5.
Symbolic
[(M - G)AG] → M
Ртopоsitional
M = I'll deal with the module for an hour.
G = Il play Genshin after the module.
If Ill deal with the module for an hour, I'll play Genshin after. I played
Genshin after the module. Therefore, I've dealt with the module for an hour.
M
G
M - G
[(м — G) л G]
[(M - G)A G] - M
T
T
F
F
F
T
F
F
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