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Solutions courtesy of Brian Schrock…
1. ((True /\ P) \/ Q)
True is a WFF; P and Q are WFFs, therefore True /\ P is a WFF.
Since (True
/\ P) and Q are WFFs,
(True/\P)\/Q is a WFF.
TRUE
P
Q
True /\ P
((True /\ P) \/ Q)
T
F
F
F
F
T
F
T
F
T
T
T
F
T
T
T
T
T
T
T
The proposition is satisfiable but not a tautology.
2. ((P /\ Q) ==> (Q \/ P))
P and Q are WFFs.
Since P and Q are WFFs, (P /\ Q) and (Q \/ P) are WFFs.
Since (P /\ Q) and (Q \/ P) are WFFs, ((P /\ Q)=>(Q \/ P)) is a WFF.
P
Q
P /\ Q
Q \/ P
((P /\ Q) ==> (Q \/ P))
F
F
F
F
T
F
T
F
T
T
T
F
F
T
T
T
T
T
T
T
The proposition is a tautology.
3. (((P \/ Q) /\ (P \/ R)) <=> (P /\ (Q \/ R)))
P, Q, and R are WFFs.
Since P, Q, and R are WFFs, (P \/ Q), (P \/ R), and (Q \/ R) are WFFs.
Since P and (Q \/ R) are WFFs, (P /\ (Q \/ R)) is a WFF.
Since (P \/ Q) and (P \/ R) are WFFs, ((P \/ Q) /\ (P \/ R)) is a WFF.
Since ((P \/ Q) /\ (P \/ R)) and (P /\ (Q \/ R)) are WFFs, (((P \/ Q) /\ (P \/ R))
<=> (P /\ (Q \/ R))) is a
WFF.
P
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This homework help was uploaded on 04/08/2008 for the course CS 2603 taught by Professor Rexpage during the Spring '08 term at The University of Oklahoma.
 Spring '08
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