## Chapter 13: PROPOSITIONAL LOGIC - ARGUMENTS - Practice, Part B -

Multiple Choice:
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No. of Questions = 31

This is an exercise in recognizing the equivalence rules of propositional logic. You will be given two statements, and must give the name of the rule that says the two statements are equivalent. Use the standard abbreviations for the rules:

Tautology: Taut
Double negation: DN
Commutation: Com
Association: Assoc
Distribution: Dist
De Morgan's Law: DM
Contrapositive: Contra
Implication: Imp
Biconditional: Bicon
Exportation: Exp

The following symbols have been used:

A tilde (~)indicates negation.
A lower-case "v" (v) indicates "or."
A greater-than symbol (>)indicates "if-then."
An asterisk (*) indicates "and."
An equals sign (=) indicates "if and only if."

This exercise has two levels of difficulty: (a) questions 1-16 and (b) questions 17-32.

 1. 1. R*S2. S*R a) Taut b) DN c) Com d) Assoc e) Dist 2. 1. ~(AvB)2. ~A*~B a) DM b) Contra c) Imp d) Bicon e) Exp 3. 1. D2. DvD a) Taut b) DN c) Com d) Assoc e) Dist 4. 1. F>G2. ~G>~F a) DM b) Contra c) Imp d) Bicon e) Exp 5. 1. K>L2. ~KvL a) DM b) Contra c) Imp d) Bicon e) Exp 6. 1. Q2. ~~Q a) Taut b) DN c) Com d) Assoc e) Dist 7. 1. A*(BvC)2. (A*B)v(A*C) a) Taut b) DN c) Com d) Assoc e) Dist 8. 1. D>(E>F)2. (D*E)>F a) DM b) Contra c) Imp d) Bicon e) Exp 9. 1. M=N2. (M>N)*(N>M) a) DM b) Contra c) Imp d) Bicon e) Exp 10. 1. ~~(D*F)2. D*F a) Taut b) DN c) Com d) Assoc e) Dist 11. 1. ~H>K2. ~K>~~H a) DM b) Contra c) Imp d) Bicon e) Exp 12. 1. Qv(~P*R)2. (Qv~P)*(QvR) a) Taut b) DN c) Com d) Assoc e) Dist 13. 1. (F*G)v(H>I)2. (H>I)v(F*G) a) Taut b) DN c) Com d) Assoc e) Dist 14. 1. (K*~L)v(~K*~~L)2. K=~L a) DM b) Contra c) Imp d) Bicon e) Exp 15. 1. (PvQ)vR2. Pv(QvR) a) Taut b) DN c) Com d) Assoc e) Dist 16. 1. (D*F)>G2. ~G>~(D*F) a) DM b) Contra c) Imp d) Bicon e) Exp 17. 1. ~[(J*K)*~I)2. ~(J*K)v~~I a) DM b) Contra c) Imp d) Bicon e) Exp 18. 1. [A*(B*C)]>D2. [(A*B)*C]>D a) Taut b) DN c) Com d) Assoc e) Dist 19. 1. (DvE)>F2. ~[(DvE)*~F] a) DM b) Contra c) Imp d) Bicon e) Exp 20. 1. [(AvB)*C]>D2. (AvB)>(C>D) a) DM b) Contra c) Imp d) Bicon e) Exp 21. 1. [Ev(F*G)]v(H>J)2. [(EvF)*(EvG)]v(H>J) a) Taut b) DN c) Com d) Assoc e) Dist 22. 1. A>~(B*~D)2. [A>~(B*~D)]v[A>~(B*~D)] a) Taut b) DN c) Com d) Assoc e) Dist 23. 1. ~(RvS)>[~O*(PvQ)]2. ~(RvS)>[~O*(~~PvQ)] a) Taut b) DN c) Com d) Assoc e) Dist 24. 1. (A>B)v[B*(C=D)]2. [(A>B)vB]*[(A>B)v(C=D)] a) Taut b) DN c) Com d) Assoc e) Dist 25. 1. ~[(EvF)*(G>H)]2. ~(EvF)v~(G>H) a) DM b) Contra c) Imp d) Bicon e) Exp 26. 1. ~(AvB)>[C*(DvF)]2. ~~(AvB)v[C*(DvF)] a) DM b) Contra c) Imp d) Bicon e) Exp 27. 1. [(E>F)>(GvH)]*[(GvH)>(E>F)]2. (E>F)=(GvH) a) DM b) Contra c) Imp d) Bicon e) Exp 28. 1. (~AvB)>[~(CvD)*(D>B)]2. (~AvB)>[(~C*~D)*(D>B)] a) DM b) Contra c) Imp d) Bicon e) Exp 29. 1. [(F*G)v(~F*~G)]v(G>H)2. (F*G)v[(~F*~G)v(G>H)] a) Taut b) DN c) Com d) Assoc e) Dist 30. 1. [(IvJ)*(K>L)]>(J>L)2. (IvJ)>[(K>L)>(J>L)] a) DM b) Contra c) Imp d) Bicon e) Exp 31. 1. [(M*N)v~(N*~R)]>S2. [(M*N)v(N>R)]>S a) DM b) Contra c) Imp d) Bicon e) Exp