Practice With Long Truth-Tables
Construct a long truth-table for each of the arguments, and then determine whether the argument is valid. Answers follow the exercises.
1.
P1 P & Q
P2 P v Q
C P -> Q2.
P1 P -> Q
P2 ~P
C ~Q3.
P1 Q v P
P2 P -> (Q -> P)
C P <-> Q4.
P1 Q
C Q v Q5.
P1 (P & Q) -> (P v Q)
P2 ~P
P3 ~Q
C ~ (P -> Q)6.
P1 P -> (Q -> R)
P2 ~(Q v R)
C ~P7.
P1 ~(P <-> Q)
P2 ~(P -> (Q -> P))
C R8.
P1 P -> R
P2 ~R v (P v R)
P3 P -> ~(P v R)
C ~P9.
P1 P -> (P <-> Q)
P2 Q & (P v Q)
C ~~P10.
P1 G -> S
P2 S v G
C G & S
ANSWERS:1. valid
P1 | P2 | C | ||
P | Q | P & Q | P v Q | P -> Q |
T | T | T | T | T |
T | F | F | T | F |
F | T | F | T | T |
F | F | F | F | T |
2. invalid (third row)
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3. invalid (rows 2 and 3)
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4. valid
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5. invalid (row 4)
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(P v Q) |
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6. invalid (row 4)
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7. valid
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8. valid
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9. valid
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10. invalid (row 3)
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