Logic as a tool a guide to formal logical reasoning ( PDFDrive ) 302

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Logic as a Tool

The rule is not sound, hence the argument is not correct.
(p ∧ q) → r : T , r → p : T , ¬q : T , ơr : F
q:F
r:T
r:F
ì

p:T
r:T

pq :F
p:F
ì

q:F

(d) Denote Socrates is wise by p, “Socrates is happy” by q , and “Socrates is a
philosopher” by r . Then the inference rule on which the argument is based is:

p ∨ ¬q, ¬p → ¬r
.
r → ¬q
The rule is not sound, hence the argument is not correct.
p ∨ ¬q : T , ¬p → ¬r : T , r → ¬q : F
r : T , ơq : F
q:T
ơq : T

q:F
ì

p:T
ơp : F

ơr : T

p:T

r:F