Part I Proof in Propositional Logie Show that each of the fellowing arguments is valid by constructing a proef. Symbola for you to copy and paste 2,v 1. (Ev F)G H.-E
Part I Proof in Propositional Logie Show that each of the fellowing arguments is valid by constructing a proef. Symbola for you to copy and paste 2,v 1. (Ev F)G H.-E
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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Part I Proof in Propositional Logic
Show that each of the following arguments is valid by constructing a proof.
7. Nothing is lost.
8. Not every law is enforced.
9. Every professor can go home only if all the work is done.
Symbols for you to copy and paste: 2, V, ~, -, =
1.
Part III Proof in Predicate Logic
(Ev F) - G
Construct a proof for the following arguments. |
-G
1.
-H=F
H--E
Ba (x) (Cx- Dx)
Ca- Ba
Da
2. (Hint: use Reductio ad Absurdum)
(F- G) -H
-F
(3x)Kx = (x) (Lx- Mx)
Kb - Lb
H
Mb
3.
(A v B) = [C . D) = E]
B.C
E- F v G)
(B= -F) . (C =-G)
D
-The End-
Part II Symbolization
Put the following statements into symbolic notation, using the highlighted letters as
predicates.
(Existential quantifier: 3x)
1. If New York is a city, it has a mayor. (Note: in this case, it is the convention that we use
lower case "n" to refer to the subject of a singular statement, ie the city of New York.
The same applies to no. 2 below.)
2. Japan is not a city.
3. Some people are not sensible.
4. Every physical object has a size and a mass.
5. If one of the tourists is late, all the tourists on the bus must wait.
6. If everything is physical, then there are no ghosts.
2
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Part I Proof in Propositional Logic
Show that each of the following arguments is valid by constructing a proof.
7. Nothing is lost.
8. Not every law is enforced.
9. Every professor can go home only if all the work is done.
Symbols for you to copy and paste: 2, V, ~, -, =
1.
Part III Proof in Predicate Logic
(Ev F) - G
Construct a proof for the following arguments. |
-G
1.
-H=F
H--E
Ba (x) (Cx- Dx)
Ca- Ba
Da
2. (Hint: use Reductio ad Absurdum)
(F- G) -H
-F
(3x)Kx = (x) (Lx- Mx)
Kb - Lb
H
Mb
3.
(A v B) = [C . D) = E]
B.C
E- F v G)
(B= -F) . (C =-G)
D
-The End-
Part II Symbolization
Put the following statements into symbolic notation, using the highlighted letters as
predicates.
(Existential quantifier: 3x)
1. If New York is a city, it has a mayor. (Note: in this case, it is the convention that we use
lower case "n" to refer to the subject of a singular statement, ie the city of New York.
The same applies to no. 2 below.)
2. Japan is not a city.
3. Some people are not sensible.
4. Every physical object has a size and a mass.
5. If one of the tourists is late, all the tourists on the bus must wait.
6. If everything is physical, then there are no ghosts.
2
Page 2 of 2
264 words
Text Predictions: On
Accessibility: Good to go
D Focus
60%
43°F
12:09 PM
w
Sunny
4/19/2022
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