Chapter 10 Deductive Arguments II Answer Key
Short Answer Questions
1.
Using the letters provided below, symbolize this claim: “If we plant from seed, we’ll have to
plant annuals.”
A = We plant annuals.
S = We plant from seed.
S → A
2.
Using the letters provided below, symbolize this claim: “We can plant perennials only if we
plant from cuttings.”
P = We plant perennials.
C = We plant from cuttings.
P → C
3.
Using the letters provided below, symbolize this claim: “The only way we can plant from
seed is to plant annuals.”
A = We plant annuals.
S = We plant from seed.
S → A
4.
Using the letters provided below, symbolize this claim: “If we plant both annuals and
perennials, then we can plant from both seed and cuttings.”
P = We plant perennials.
A = We plant annuals.
S = We plant from seed.
C = We plant from cuttings.
(A & P) → (S & C)
5.
Using the letters provided below, symbolize this claim: “We cannot plant perennials if we
plant from either seed or from cuttings.”
P = We plant perennials.
S = We plant from seed.
C = We plant from cuttings.
(S v C) → ~P
6.
Using the letters provided below, symbolize this claim: “If we don’t plant from seed, then
we can’t plant either annuals or perennials.”
P = We plant perennials.
A = We plant annuals.
S = We plant from seed.
~S → ~(A v P)
7.
Using the letters provided below, symbolize this claim: “We can’t plant perennials unless
we plant from cuttings.”
P = We plant perennials.
C = We plant from cuttings.
8.
Using the letters provided below, symbolize this claim: “The only way we can plant both
annuals and perennials is by planting from both cuttings and seed.”
P = We plant perennials.
A = We plant annuals.
S = We plant from seed.
C = We plant from cuttings.
(A & P) → (C & S)
9.
Using the letters provided below, symbolize this claim: “Either we will plant from cuttings,
or, if we don’t plant perennials, we can plant from seed.”
P = We plant perennials.
S = We plant from seed.
C = We plant from cuttings.
C v (~P → S)
10.
Using the letters provided below, symbolize this claim: “We can plant neither perennials
nor annuals if we don’t plant from both cuttings and seed.”
P = We plant perennials.
A = We plant annuals.
S = We plant from seed.
C = We plant from cuttings.
~(C & S) → ~(P v A)
11.
Using the letters provided below, symbolize this claim: “The only way we can avoid
threatening wildlife is to avoid increasing agricultural production.”
W = Wildlife are (or will be) threatened.
A = Agricultural production is increased.
~W → ~A
12.
Using the letters provided below, symbolize this claim: “We cannot both increase
agricultural production and avoid threatening wildlife.”
W = Wildlife are (or will be) threatened.
A = Agricultural production is increased.
13.
Using the letters provided below, symbolize this claim: “If we are to increase agricultural
production, we’ll have to continue the use of pesticides, but if we do that wildlife will be
threatened.”
W = Wildlife are (or will be) threatened.
A = Agricultural production is increased.
P = The use of pesticides is continued.
(A → P) & (P → W)
14.
Using the letters provided below, symbolize this claim: “Wildlife will not be threatened
provided we do not continue the use of pesticides.”
W = Wildlife are (or will be) threatened.
P = The use of pesticides is continued.
~P → ~W
15.
Using the letters provided below, symbolize this claim: “Wildlife will be threatened if either
agricultural production is increased or pesticide use is continued.”
W = Wildlife are (or will be) threatened.
A = Agricultural production is increased.
P = The use of pesticides is continued.
16.
Using the letters provided below, symbolize this claim: “The continuation of pesticide use
will be sufficient to ensure that wildlife will be threatened.”
W = Wildlife are (or will be) threatened.
P = The use of pesticides is continued.
P → W
17.
Using the letters provided below, symbolize this claim: “The continued use of pesticides is
necessary for increased agricultural production.”
A = Agricultural production is increased.
P = The use of pesticides is continued.
A → P
18.
Using the letters provided below, symbolize this claim: “Together, the continued use of
pesticides and the increase in agricultural production will guarantee that wildlife will be
threatened.”
W = Wildlife are (or will be) threatened.
A = Agricultural production is increased.
P = The use of pesticides is continued.
19.
Using the letters provided below, symbolize this claim: “Agricultural production will not
increase even though the use of pesticides is continued.”
A = Agricultural production is increased.
P = The use of pesticides is continued.
~A & P
20.
Using the letters provided below, symbolize this claim: “While pesticide use is continued,
agricultural production will not increase.”
A = Agricultural production is increased.
P = The use of pesticides is continued.
P & ~A
21.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
Q v P
~Q → ~R/∴ R → P
P = F
22.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
~Q → P
R v S
Q → ~S/∴ R
P = T
Q = F
R = F
S = T
23.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
P v Q
P → R/∴ R → Q
P = T
Q = F
R = T
24.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
(Q & P) → R
S → ~R/∴ S → ~Q
Q = T
P = F
R = F
S = T
25.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
S → (P v R)
Q → S/∴ Q → P
S = T
P = F
R = T
Q = T
26.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
T → ~S
S v ~Q
~T → (Q v R)/∴ ~Q → R
T = T
S = F
Q = F
R = F
27.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
~R → ~Q
~P → (R & Q)/∴ P
R = T
Q = T
P = F
28.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
(Q & S) → (P v R)
T → Q
~T v S/∴ T → R
Q = T
S = T
P = T
R = F
T = T
29.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
P → (Q → S)
Q v R/∴ (P & R) → S
P = T
Q = F
30.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
P → (Q v R)
~(Q → R)
S → P/∴ ~S
P = T
Q = T
R = F
S = T
31.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
P v Q
(Q & R) → S
~P → ~R/∴ R → S
P = T
Q = F
R = T
S = F
32.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
P v (Q → R)
S → ~(P v R)/∴ S → Q
P = F
Q = F
R = F
S = T
33.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
~L & S
(P v Q) → L/∴ Q v S
L = F
S = F
P = F
Q = F
34.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
P → (T & R)
(R → S) v T
~(S & Q)/∴ Q → ~P
P = T
T = T
R = T
S = F
Q = T
35.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
~P v (Q → R)
Q → (R v S)/∴ Q → (~P v S)
P = T
Q = T
36.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there are only two such assignments).
(P & Q) → (R v S)
P & Q/∴ R & S
(both are correct):
P = T P = T
Q = T Q = T
R = T R = F
S = F S = T
37.
For the following argument, assign truth values to the letters to show the argument’s
invalidity (there is only one such assignment).
P → (Q v ~R)
R & S
~S v T/∴ ~P & T
P = T
Q = T
R = T
S = T
T = T
38.
Determine which of the lettered claims below is equivalent to the following: Steve can give
blood if he has been tested. (This is easy to do if you symbolize the claims first and have
some familiarity either with truth tables or with the Group II rules for derivations—the
truth-functional equivalences.)
A. If Steve can give blood, then he has been tested.
B. If Steve has been tested, then he can give blood.
C. Steve cannot give blood, and he has not been tested.
D. Steve has not been tested, but he can give blood.
Equivalent to B
39.
Determine which of the lettered claims below is equivalent to the following: It’s sufficient
for Steve to be tested in order for him to give blood. (This is easy to do if you symbolize
the claims first and have some familiarity either with truth tables or with the Group II rules
for derivations—the truth-functional equivalences.)
A. If Steve can give blood, then he has been tested.
B. If Steve has been tested, then he can give blood.
C. Steve cannot give blood, and he has not been tested.
D. Steve has not been tested, but he can give blood.
Equivalent to B
40.
Determine which of the lettered claims below is equivalent to the following: Although
Steve can give blood, he has not been tested. (This is easy to do if you symbolize the
claims first and have some familiarity either with truth tables or with the Group II rules for
derivations—the truth-functional equivalences.)
A. If Steve can give blood, then he has been tested.
B. If Steve has been tested, then he can give blood.
C. Steve cannot give blood, and he has not been tested.
D. Steve has not been tested, but he can give blood.
Equivalent to D
41.
Determine which of the lettered claims below is equivalent to the following: It’s necessary
for Steve to be tested in order for him to give blood. (This is easy to do if you symbolize
the claims first and have some familiarity either with truth tables or with the Group II rules
for derivations—the truth-functional equivalences.)
A. If Steve can give blood, then he has been tested.
B. If Steve has been tested, then he can give blood.
C. Steve cannot give blood, and he has not been tested.
D. Steve has not been tested, but he can give blood.
Equivalent to A
42.
Determine which of the lettered claims below is equivalent to the following: Steve can
neither be tested nor give blood. (This is easy to do if you symbolize the claims first and
have some familiarity either with truth tables or with the Group II rules for derivations—the
truth-functional equivalences.)
A. If Steve can give blood, then he has been tested.
B. If Steve has been tested, then he can give blood.
C. Steve cannot give blood, and he has not been tested.
D. Steve has not been tested, but he can give blood.
Equivalent to C
43.
Determine which of the lettered claims below is equivalent to the following: If the gun has
a trigger lock, then it can be sold. (This can be easy to do if you symbolize the claims first
and have some familiarity either with truth tables or with the Group II rules for
derivations—the truth-functional equivalences.)
A. Only if the gun has a trigger lock can it be sold.
B. The gun has no trigger lock, but it can be sold anyway.
C. If the gun cannot be sold, then it has no trigger lock.
D. If the gun has no trigger lock, then it can be sold.
Equivalent to C.
10–20
44.
Determine which of the lettered claims below is equivalent to the following: The gun
cannot be sold unless it has a trigger lock. (This can be easy to do if you symbolize the
claims first and have some familiarity either with truth tables or with the Group II rules for
derivations—the truth-functional equivalences.)
A. Only if the gun has a trigger lock can it be sold.
B. The gun has no trigger lock, but it can be sold anyway.
C. If the gun cannot be sold, then it has no trigger lock.
D. If the gun has no trigger lock, then it can be sold.
Equivalent to A
45.
Determine which of the lettered claims below is equivalent to the following: If the gun
cannot be sold, then it does have a trigger lock. (This can be easy to do if you symbolize
the claims first and have some familiarity either with truth tables or with the Group II rules
for derivations—the truth-functional equivalences.)
A. Only if the gun has a trigger lock can it be sold.
B. The gun has no trigger lock, but it can be sold anyway.
C. If the gun cannot be sold, then it has no trigger lock.
D. If the gun has no trigger lock, then it can be sold.
Equivalent to D