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). T $\rarr$ ~S S v ~Q ~T $\rarr$ (Q v R)/ $\therefore$ ~Q $\rarr$ R

Use the short truth-table method to determine whether the following is valid or invalid: M $\rarr$ (N $\rarr$ O) (~N v O) $\rarr$ ~P P/ $\therefore$ ~M

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

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) R & S ~S v T/ $\therefore$ ~P & T

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

Determine whether the following is valid or invalid: If the current economic policies were to put an end to the recession,then the administration would deserve a round of applause.But there can be no end to the recession without the creation of a large number of decent-paying jobs.It follows,then,that the only way the administration is going to get a round of applause is if a large number of decent-paying jobs get created.

Determine which of the lettered claims below is equivalent to the following:If the gun has a trigger lock,then it can be sold.(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. )

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.

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

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

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) Q $\rarr$ (R v S)/ $\therefore$ Q $\rarr$ (~P v S)

Determine whether the following is valid or invalid: Look,if the check bounced,then you're right:Two things happened.First,we'd owe a penalty.And second,our records would be out of whack.Now,if our records are out of whack or if we pay a penalty-either way-then we're in big trouble,just like you said.The check isn't gonna bounce,though.So relax.We're not in any trouble.

Using the letters provided below,symbolize this claim:"The only way we can avoid threatening wildlife is to avoid increasing agricultural production." W = Wildlife are (or will be)threatened. A = Agricultural production is increased.

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

Use the short truth-table method to determine whether the following is valid or invalid: A $\rarr$ B ~C v D E $\rarr$ F G $\rarr$ H A v C E v G/ $\therefore$ (B v D)v (F v H)

Using the letters provided below,symbolize this claim:"Wildlife will be threatened if either agricultural production is increased or pesticide use is continued." W = Wildlife are (or will be)threatened. A = Agricultural production is increased. P = The use of pesticides is continued.

Using the letters provided below,symbolize this claim:"If we plant both annuals and perennials,then we can plant from both seed and cuttings." 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). ~L & S (P v Q) $\rarr$ L/ $\therefore$ Q v S

Determine which of the lettered claims below is equivalent to the following:If the gun cannot be sold,then it does have 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. ) A.Only if the gun has a trigger lock can it be sold. B.The gun has no trigger lock,but it can be sold anyway. C.If the gun cannot be sold,then it has no trigger lock. D.If the gun has no trigger lock,then it can be sold. Equivalent to D

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