Exam 10: Decentralization and Performance Evaluation

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

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.

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.

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.

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.

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.

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.

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

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

For the following argument, assign truth values to the letters to show the argument's invalidity (there are only two such assignments). (A & Y) → (I v J) A & Y/∴ I & J

Determine whether the following is valid or invalid: It's not that Alberto and John will both attend the meeting. I did learn, however, that if either Susan or Allene goes, John plans to go for sure. Therefore, if Alberto goes, it means neither Susan nor Allene is going.

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

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

Determine whether the following is valid or invalid: I finally discovered the mystery of why hard beds are good for you. Here's the story: If you have a hard bed, then you cannot stay comfortable for long periods, and when you can't stay comfortable for long periods, you roll around a lot. If you roll around a lot, then your joints don't ache from being in one position for too long. Therefore, if your joints ache in the morning from sleeping too long in one position, then you don't have a hard bed.

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.

For the following argument, assign truth values to the letters to show the argument's invalidity (there is only one such assignment). ~U & G (H v C) → U/∴ C v G

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

Determine whether the following is valid or invalid: In a class like this, it's necessary to work a lot of problems on your own in order to be familiar with the material, and such familiarity is necessary to do well in the exams. So if you work a lot of problems on your own, you'll do well on the exams.

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.

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.)