Deck 10: Decentralization and Performance Evaluation

Question 1

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.

Answer 1

~(A & ~W)

Question 2

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.

Answer 2

~S → ~(A v P)

Question 3

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.

Answer 3

(A & P) → (S & C)

Question 4

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.

Question 5

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.

Question 6

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.

Question 7

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.

Question 8

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.

Question 9

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.

Question 10

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.

Question 11

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.

Question 12

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.

Question 13

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.

Question 14

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.

Question 15

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.

Question 16

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.

Question 17

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.

Question 18

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.

Question 19

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.

Question 20

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.

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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.

Question 26

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

Question 27

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.

Question 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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.

Question 34

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)

Question 35

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

Question 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P v (R & ~S)
Q → ~P/∴ Q → S

Question 42

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
(T v Q) → R
~R/∴ ~Q

Question 43

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.

Question 44

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.

Question 45

Use the short truth-table method to determine whether the following is valid or invalid:
P → Q
~(Q & ~R)
~R v S
~(S & ~T)
T/∴ P

Question 46

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.

Question 47

Use the short truth-table method to determine whether the following is valid or invalid:
A → B
C → D
~(~A & ~C)/∴ ~B → (D & ~B)

Question 48

Use the short truth-table method to determine whether the following is valid or invalid:
M → (N → O)
(~N v O) → ~P
P/∴ ~M

Question 49

Use the short truth-table method to determine whether the following is valid or invalid:
~E v ~D
~(A → C)
~(~B v ~E)
~(A & B) v (C → __________D)/∴ ~A

Question 50

Determine which of the lettered claims below is equivalent to the following: The gun can be sold even though it has no 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.

Question 51

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.

Question 52

Use the short truth-table method to determine whether the following is valid or invalid:
A → B
C → D
B v D/∴ A v C

Question 53

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P → (Q v R)
~S v ~T
(Q v R) → (S & T)/∴ ~P

Question 54

Use the short truth-table method to determine whether the following is valid or invalid:
P → (Q & R)
R → (T v S)
~T v (U & ~W)
P/∴ ~W

Question 55

Use the short truth-table method to determine whether the following is valid or invalid:
P → Q
Q → R
R → S
P/∴ S v T

Question 56

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.

Question 57

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
~P → (Q & R)
P → ~S
Q v R/∴ ~S

Question 58

Use the short truth-table method to determine whether the following is valid or invalid:
A → B
~D → ~C
~D
~C → ~B/∴ ~A

Question 59

Use the short truth-table method to determine whether the following is valid or invalid:
A → B
~C v D
E → F
G → H
A v C
E v G/∴ (B v D) v (F v H)

Question 60

Use the short truth-table method to determine whether the following is valid or invalid:
P → Q
~Q v R
~(R & ~S)
~P/∴ ~S

Question 61

Determine whether the following is valid or invalid:
If he doesn't think he'll pass the class, then either he'll be talking to someone, or he won't be paying attention, or both. Well, look at him. He's talking to someone. And he's not paying the least bit of attention. Clearly he doesn't think he'll pass the class.

Question 62

Determine whether the following is valid or invalid:
If she can play the tuba, then she can darn well play the baritone. And if she can play the baritone, then she can play the French horn. We can conclude that as she can play the tuba, she can play the French horn.

Question 63

Symbolize the following argument, and test it for validity. If valid, construct a deduction;
if invalid, assign truth values that show that the premises can be while the conclusion is . Use these letters: D = The drought will continue.; S = We get an early storm.;
M = Managers of the ski areas will be happy.; F = There will be great fire danger next year.
Unless an early storm moves in, the drought will continue, and there will be great danger of fire next year.
But the drought is not going to continue. Therefore, there will not be a great danger of fire next year.

Question 64

Symbolize the following argument, and test it for validity. If valid, construct a deduction;
if invalid, assign truth values that show that the premises can be while the conclusion is . Use these letters: D = The drought will continue; S = We get an early storm;
M = Managers of the ski areas will be happy; F = There will be great fire danger next year.
The drought will continue if we don't get a storm. If we do get a storm, the managers of the ski areas will be happy. Since we'll either get a storm or we won't, it follows that either the drought will continue or the ski area managers will be happy.

Question 65

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
(Q & R) → P
(R → P) → S
Q/∴ S

Question 66

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
(P v Q) → (C & D)
~C/∴ ~Q

Question 67

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P v (Q & K)
(P v Q) → [(L → ~X) & (~X → L)]
(L → ~X) → (X & ~Y)
(Y → Z) & (Z → M)
(Q → K) → Z/∴ Z

Question 68

Symbolize the following argument, and test it for validity. If valid, construct a deduction;
if invalid, assign truth values that show that the premises can be while the conclusion is . Use these letters: D = The drought will continue; S = We get an early storm;
M = Managers of the ski areas will be happy; F = There will be great fire danger next year.
If there's no early storm, the drought will continue. And if the drought continues, there will be a great danger of fire next year. So, if there is to be no great danger of fire next year, there must be an early storm.

Question 69

Determine whether the following is valid or invalid:
It's easy enough to do logic if you think logically. Fortunately, I have no trouble doing logic, so I guess I think logically.

Question 70

Determine whether the following is valid or invalid:
She must not have ordered the eggplant, 'cause if she had ordered it, then she wouldn't be eating any dessert like she's doing right now.

Question 71

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P → Q
Q → R
R → S
(P → S) → (Q → ~P)
~P/∴ ~Q

Question 72

Symbolize the following argument, and test it for validity. If valid, construct a deduction;
if invalid, assign truth values that show that the premises can be while the conclusion is . Use these letters: D = The drought will continue; S = We get an early storm;
M = Managers of the ski areas will be happy; F = There will be great fire danger next year.
There will be a great danger of fire next year only if the drought continues, and it will continue unless we get an early storm. However, if we do get an early storm, the ski area managers will be happy. So if the ski area managers are not happy, it'll mean that there's going to be a great danger of fire next year.

Question 73

Determine whether the following is valid or invalid:
Look, if the check bounced, then you're right: Two things will happen. First, we'd owe a penalty. And second, our records would be out of whack. Now, if our records are out of whack or if we pay a penalty-either way-then we're in big trouble, just like you said. The check isn't going to bounce, though. So relax. We're not in any trouble.

Question 74

Determine whether the following is valid or invalid:
If we don't see the movie tonight, we won't be able to talk about it in class. And if we can't talk about it in class, we won't make Ms. Schmidt very happy. So let's see the movie. Then Ms. Schmidt will be happy.

Question 75

Determine whether the following is valid or invalid:
If it's going to be a cool spring, then the azaleas will need extra fertilizer. Indications are, however, that it's not going to be a cool spring.

Question 76

Symbolize the following argument, and test it for validity. If valid, construct a deduction;
if invalid, assign truth values that show that the premises can be while the conclusion is . Use these letters: D = The drought will continue.; S = We get an early storm.;
M = Managers of the ski areas will be happy.; F = There will be great fire danger next year.
Either there will be an early storm, or the drought will continue. If there's no continuation of the drought, then the managers of the ski areas will be happy and there will be no great danger of fire next year. So if we're to avoid any great danger of fire next year and to make the ski area managers happy, it will be necessary for there to be an early storm.

Question 77

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P v ~Q
R → Q
~P
~R → ~W/∴ W

Question 78

Determine whether the following is valid or invalid:
If a flyer is on one of the bulletin boards, then you know it was approved by the Associated Students, and that flyer was approved. Therefore, it's on one of the bulletin boards somewhere.

Question 79

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
(P → T) & S
S → (T → R)
~R/∴ ~T

Question 80

Determine whether the following is valid or invalid:
Either she ordered the eggplant, or she ordered the calamari, though possibly she might have ordered both. Well, she ordered the eggplant. So, she didn't order the calamari.