Exam 10: Deductive Arguments Ii Truth-Functional Logic

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. )

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

Using the letters provided below,symbolize this claim:"If we don't plant from seed,then we can't plant either annuals or perennials." P = We plant perennials. A = We plant annuals. S = We plant from seed.

Using the letters provided below,symbolize this claim:"While pesticide use will continue,agricultural production will not increase." A = Agricultural production is increased. P = The use of pesticides is continued.

Using the letters provided below,symbolize this claim:"We can't plant perennials unless we plant from cuttings." P = We plant perennials. C = We plant from cuttings.

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. A = Agricultural production is increased. P = The use of pesticides is continued.

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

Determine whether the following is valid or invalid: Either she ordered the eggplant,or she ordered the calamari,though possibly she might have ordered both.Well,she ordered the eggplant.So,she didn't order the calamari.

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 $\rarr$ ~P/ $\rarr$ Q $\rarr$ S

Determine whether the following is valid or invalid: She must not have ordered the eggplant,'cause if she 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). Q v P ~Q $\rarr$ ~R/ $\therefore$ R $\rarr$ P

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.

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

Using the letters provided below,symbolize this claim:"We can plant perennials only if we plant from cuttings." P = We plant perennials. C = We plant from cuttings.

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

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

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 P $\rarr$ R/ $\therefore$ R $\rarr$ 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 derivations-the truth-functional equivalences. )