Propositional Logic Worksheet
Part 1 – Using information from this week’s lesson and last week’s Rules for Translating
Ordinary Language, translate the following sentences into symbolic form using capital
letters to represent affirmative statements. All examples are from Hurley, pp 319-322. [If
you do not have the dot, use & for “and” and > or “if, then”]. Each correct answer is
worth 2.5 points. Partial credit is possible.
1. Arizona has a national park, but Nebraska does not.
Answer: A • ~ N
2. If Chanel has a Rosewood fragrance then so does Lanvin.
Answer: C  L
3. Mercedes will introduce a hybrid model only if Lexis and BMW do.
Answer: (L • B)  M
4. Either Sonia Sotomayor or Antonin Scalia have a modern approach to the
Constitution, but it is not the case that both do.
Answer: (S • A) v ~ (S • A)
5. If health maintenance organizations cut costs, then either preventive medicine is
emphasized or the quality of care deteriorates.
Answer: a > (b v c)
6. If evolutionary biology is correct, then higher lifeforms arose by chance, and if that is
so, then it is not the case that there is any design in nature and divine providence is a
myth.
Answer: (E -> H) & [H -> (~ D & P)]
7. Neither Ferrari nor Maserati makes economy cars.
Answer: ~(F∨M)
8. Either Nokia or Seiko make cell phones
Answer: N v S
9. Saturn has rings and Neptune is windy, or Jupiter is massive.
Answer: (S • N) v J
10. if Sax promotes gift cards, then either Macy’s or Bloomingdale’s puts on a fashion
show:
Answer: S(MvB)
Part 2 – For the following arguments, construct a truth table to determine validity. The
tables will be created for you, but you will need to work out the contents. For this
component, the problems are from Jackson and Newberry. Each correct answer is
worth 10 points. Partial credit is possible. See questions 1 and 3 for examples on how to
lay out the argument in the grid
1. S > C
~S
~C
S
C
S
>
T
T
T
T
T
F
T
F
F
T
F
T
F
F
F
T
This argument is: invalid
C
T
F
T
F
/
/
/
/
~
F
F
T
/ T
S
T
T
F
F
//
~
F
T
F
T
C
T
F
T
F
2. ~C > D
D
C
C
D
~
T
T
F
T
F
F
F
T
T
F
F
T
This argument is: invalid
C
T
T
F
F
>
D
/
/
/
/
/
D
//
C
T
F
T
F
3. K v L
K>M
L>M
M
K
T
T
T
T
F
F
F
F
L
M
K
v
T
T
T
v
T
F
T
v
F
T
T
v
F
F
T
v
T
T
T
v
T
F
T
v
F
T
F
v
F
F
F
v
This argument is: valid
L
T
T
T
T
T
T
F
F
/
K
>
M
/
L
>
M
//
M
4. P > Q
R&Q
R>P
P
Q
R
P
>
Q
/
R
&
This argument is: Invalid
5. E > F
F>G
E>G
E
F
G
E>F
T
T
T
T
T
T
F
T
T
F
T
F
T
F
F
F
F
T
T
T
F
T
F
T
F
F
T
T
F
F
F
T
This argument is: Valid
/
/
/
/
/
/
/
/
/
F>G
T
F
T
T
T
F
T
T
//
//
//
//
//
//
//
//
//
E>G
T
F
T
F
T
T
T
T
Q
//
R
>
p
Part 3 – For the following arguments write the argument, using the symbols provided in
Well Formed Formulas. Then, on you own use either a full or indirect truth table to help
you determine the argument’s validity. You do not need to provide the table. Each is
worth 5 points. Partial credit is possible.
1. Anis’s mom said that he will go to Disneyland only if he finishes all his homework. I
guess he’s going to Disneyland then, because he finished all his homework. (D, F)
The WFF: D > F / F // D
Is the argument valid? No, the argument is not valid
2. We won’t have good government unless qualified people are elected. This means
that we won’t have good government. After all, didn’t you see who got elected? (Q,
G)
The WFF:
Is the argument valid?
3. Should the judge remove herself from the case? I don’t think so. This is because if
she should remove herself, she must either have a conflict of interest or be ill, and this
judge has both a conflict of interest and is ill. (R, C, I)
The WFF:
Is the argument valid?
4. If the defendant’s fingerprints were on the murder weapon, then the defendant is
guilty of murder. Therefore, the defendant is guilty of murder since the forensics
expert testified that the defendant’s fingerprints were found on the murder weapon.
(F, G)
The WFF: F > G
Is the argument valid? Yes, the argument is valid
5. There’s a great deal of controversy on the issue of global warming. However, either
global warming is a reality or leading climatologists are delusional. Thus, global
warming is a reality because leading climatologists are not delusional. (R, G)
The WFF:
Is the argument valid? Yes, the argument is valid