Exam 10: Deductive Arguments Ii Truth-Functional Logic

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

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.

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.

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 on the exams.So if you work a lot of problems on your own,you'll do well on the exams.

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

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

For the following argument,assign truth values to the letters to show the argument's invalidity (there is only one such assignment). (Q & S) $\rarr$ (P v R) T $\rarr$ Q ~T v S/ $\therefore$ T $\rarr$ R

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.

Use the short truth-table method to determine whether the following is valid or invalid: P $\rarr$ Q Q $\rarr$ R R $\rarr$ S P/ $\therefore$ S v T

Use the short truth-table method to determine whether the following is valid or invalid: A $\rarr$ B ~D $\rarr$ ~C ~D ~C $\rarr$ ~B/ $\therefore$ ~A

Determine whether the following is valid or invalid: It's time to leave when they start putting up the chairs,as they're doing right now.

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.

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 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 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: A $\rarr$ B C $\rarr$ D B v D/ $\therefore$ A v C

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.

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.

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

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