Exam 10: Deductive Arguments Ii Truth-Functional Logic

Determine whether the following is valid or invalid: Either the bank made a mistake,or none of this month's deposits have been recorded.If our accountant is correct,then all the accounts have been reconciled.If it is not the case that none of the month's deposits has been recorded,then all the accounts could not have been reconciled.I have checked with our accountant,and he is indeed correct.Therefore,the only alternative is that the bank made a mistake.

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 she can play the tuba,therefore,she can play the French horn.

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 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.

For the following argument,assign truth values to the letters to show the argument's invalidity (there is only one such assignment). P $\rarr$ (Q $\rarr$ S) Q v R/ $\therefore$ (P & R) $\rarr$ S

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.

For the following argument,assign truth values to the letters to show the argument's invalidity (there is only one such assignment). ~Q $\rarr$ P R v S Q $\rarr$ ~S/ $\therefore$ R

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. )

Determine whether the following is valid or invalid: It's not true 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.

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) $\rarr$ S ~P $\rarr$ ~R/ $\therefore$ R $\rarr$ S

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 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.

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. )

For the following argument,assign truth values to the letters to show the argument's invalidity (there is only one such assignment). P $\rarr$ (Q v R) ~(Q $\rarr$ R) S $\rarr$ P/ $\therefore$ ~S

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.

Using the letters provided below,symbolize this claim:"Agricultural production will not increase even though the use of pesticides will continue." 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). P $\rarr$ (T & R) (R $\rarr$ S)v T ~(S & Q)/ $\therefore$ Q $\rarr$ ~P

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,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: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. )

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

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.

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.