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Q:
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 true while the conclusion is false. 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 theres 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 were 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
Q:
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 true while the conclusion is false. 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, itll mean that theres going to be a great danger of fire next year.
Q:
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 true while the conclusion is false. 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 theres 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.
Q:
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 true while the conclusion is false. 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.
Q:
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 true while the conclusion is false. 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 dont get a storm. If we do get a storm, the managers of the ski areas will be happy. Since well either get a storm or we wont, it follows that either the drought will continue or the ski area managers will be happy.
Q:
Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P v (Q & K)
Q:
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)
Q:
Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P → Q
Q:
Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P v ~Q
Q:
Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
(Q & R) → P
Q:
Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
(P → T) & S
Q:
Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
(T v Q) → R
Q:
Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
~P → (Q & R)
Q:
Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction.
P → (Q v R)
Q:
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:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P → (Q & R) (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P → (Q & R) (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P → (Q & R) (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. (P → Q) & (R → S) (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P → (Q → R) (Premise)/∴ Q → (P → R)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P v (Q & P) (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P → ~(M & R) (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. (M v P) → Q (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P v (Q & R) (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P v ~Q (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P → Q (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P v Q (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. (P v Q) & (P v R) (Premise)
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. ~(P v Q) (Premise)/∴ ~Q
Q:
Using rules from both Group I and Group II, construct a deduction to prove that the following is valid.
1. P & Q (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. (P v Q) → M (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. (P v Q) → (X & Z) (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. Q → (P → R) (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. P → M (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. ~P & Q (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. P → (S v T) (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. (R v Q) & S (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. (P & Q) → (R v S) (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. P → Q (Premise)
Q:
Using only rules from Group I, provide a deductive proof demonstrating the validity of the following:
1. P → (Q & R) (Premise)
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
M → (N → O)
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
P → Q
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
P → (Q & R)
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
P → Q
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
~E v ~D
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
A → B
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
A → B
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
A → B
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
A → B
Q:
Use the short truth-table method to determine whether the following is valid or invalid:
P → Q
Q:
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 derivationsthe 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.
Q:
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 derivationsthe 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.
Q:
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 derivationsthe 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.
Q:
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 derivationsthe 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.
Q:
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 derivationsthe 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.
Q:
Determine which of the lettered claims below is equivalent to the following: Its 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 derivationsthe 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.
Q:
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 derivationsthe 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.
Q:
Determine which of the lettered claims below is equivalent to the following: Its 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 derivationsthe 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.
Q:
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 derivationsthe 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.
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
P → (Q v ~R)
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there are only two such assignments).
(P & Q) → (R v S)
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
~P v (Q → R)
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
P → (T & R)
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
~L & S
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
P v (Q → R)
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
P v Q
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
P → (Q v R)
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
P → (Q → S)
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).(Q & S) → (P v R)T → Q
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
~R → ~Q
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
T → ~S
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
S → (P v R)
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
(Q & P) → R
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
P v Q
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
~Q → P
Q:
For the following argument, assign truth values to the letters to show the arguments invalidity (there is only one such assignment).
Q v P
Q:
Using the letters provided below, symbolize this claim: "While pesticide use is continued, agricultural production will not increase."
A = Agricultural production is increased.
Q:
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.
Q:
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.
Q:
Using the letters provided below, symbolize this claim: "The continued use of pesticides is necessary for increased agricultural production."
A = Agricultural production is increased.