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*S
2. 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. D
2. DvD
a) Taut
b) DN
c) Com
d) Assoc
e) Dist
4 1. F>G
2. ~G>~F
a) DM
b) Contra
c) Imp
d) Bicon
e) Exp
5 1. K>L
2. ~KvL
a) DM
b) Contra
c) Imp
d) Bicon
e) Exp
6 1. Q
2. ~~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=N
2. (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>K
2. ~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)vR
2. Pv(QvR)
a) Taut
b) DN
c) Com
d) Assoc
e) Dist
16 1. (D*F)>G
2. ~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)]>D
2. [(A*B)*C]>D
a) Taut
b) DN
c) Com
d) Assoc
e) Dist
19 1. (DvE)>F
2. ~[(DvE)*~F]
a) DM
b) Contra
c) Imp
d) Bicon
e) Exp
20 1. [(AvB)*C]>D
2. (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)]>S
2. [(M*N)v(N>R)]>S
a) DM
b) Contra
c) Imp
d) Bicon
e) Exp



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