Today’s Topics Review of Sample Test # 2 A Little Meta Logic

1)If an argument is valid, then its premises must be true. False 2) If, from an assumption, you can derive a WFF, then you may derive a conditional whose antecedent is the assumption and whose consequent is the WFF derived. TRUE 3) The English expression "only if" introduces the consequent of a conditional. TRUE 4) An argument with contradictory premises is guaranteed to be valid. TRUE 5) Two valid arguments whose conclusions contradict one another cannot both be sound. TRUE

An argument with contradictory premises is guaranteed to be valid because anything follows from a contradiction. If the premises contain a contradiction, any conclusion would follow from them. (Consider IP)

Statement forms a){[(~P v Q)  R]  (Q  ~T)} conditional b)~{[(P v Q)  R]  (Q  ~T)} negation c)([(~P v Q)  R]  Q)  ~T biconditional d)(~P v Q)  [R  (Q  ~T)] conjunction e)~P v {Q  [R (Q  ~T)]} disjunction

Equivalence Rules ~[(A  B)  (C v D)] DeMorgan (eliminate all conjunctions) (~A v ~B) v ~ (C v D) (R  S)  (P  T)Exportation R  (S  (P  T)) or ((R  S)  P)  T A  (B  (C  D)) Implication ( all conditionals) ~A v (~B v (~C v D))

Symbolizations The IRS can exact a PENALTY from the taxpayer only if the taxpayer is guilty of FRAUD or gross NEGLIGENCE. Accordingly, if a taxpayer is not guilty of fraud and not guilty of gross negligence, then the IRS cannot exact a penalty. P  (F v N)  (~F  ~N)  ~P

MARY will join us in St. Louis unless BILL is visiting from Memphis. We would have seen Bill in RAGSDALE'S last night, if he is visiting. And we didn't. So Mary will join us in St. Louis. M v B, B  R, ~R  M

If ABRAMS is telling the truth about the Sandinistas, then the U.S. should be supporting the military effort of the CONTRAS. To support the military effort of the contras, however, it is necessary to either SUPPLY them with arms or to allow them to sell DRUGS so that they can buy arms. If we supply the arms, Congress must GRANT its permission. And the contras would be BREAKING the law if they sell drugs. Congress won't grant permission for supplying arms and the contras won't sell drugs. So Abrams is not telling the truth about the Sandinistas. A  C, C  (S v D), S  G, D  B, ~G ● ~D  ~A

Constructing Proofs 1)P  (F v N)  (~F  ~N)  ~P 2)~ ( F v N)  ~P 1 Contra 3)(~F  ~N)  ~P 2 DeM

1.~A v (C  D)  ~A 2.~(E  C) 3.E 4.~E v ~C 2 DeM 5.~C3,4 DS 6.~C v ~D5 Add 7. ~(C & D) 6 Dem 8.~A1,6 DS

~Q v ~P, ~Q  (R v ~P), R  T, P  T 1. ~Q v ~Pprove T 2. ~Q  (R v ~P) 3. R  T 4. P 5. ~Q1,4DS 6. R v ~P2,5 MP 7. R6, 4 DS 8. T3,7 MP