278 Logic as a Tool The rule is not sound, hence the argument is not correct (p ∧ q) → r : T , r → p : T , ¬q : T , ¬r : F q:F r:T r:F × p:T r:T p∧q :F p:F × 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 , ¬q : F q:T ¬q : T q:F × p:T ¬p : F ¬r : T p:T r:F