Exam 10: Decentralization and Performance Evaluation

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)

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

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

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.

For the following argument, assign truth values to the letters to show the argument's invalidity (there is only one such assignment). B v A ~B → ~N/∴ N → A

Determine whether the following symbolized argument is valid or invalid. If invalid, provide a counterexample; if valid, construct a deduction. (I → K) & M M → (K → W) ~W/∴ ~K

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

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.

For the following argument, assign truth values to the letters to show the argument's invalidity (there is only one such assignment). (B & V) → N J → ~N/∴ J → ~B

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.

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.)

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.

Use the short truth-table method to determine whether the following is valid or invalid: Z → K J → O K v O/∴ Z v J

Use the short truth-table method to determine whether the following is valid or invalid: E → N N → X X → O E/∴ O v D

Use the short truth-table method to determine whether the following is valid or invalid: A → (Z & L) L → (W v G) ~W v (D & ~E) A/∴ ~E

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.)

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

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.

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)

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