280 Logic as a Tool Then the inference rule on which the argument is based is: q → ¬p, p ∧ ¬q → r q ∨ ¬r → ¬p The rule is sound, hence the argument is correct q → ¬p : T , (p ∧ ¬q) → r : T , (q ∨ ¬r) → ¬p : F q ∨ ¬r : T , ¬p : F p:T ¬p : T q:F ¬r : T q:T × p:F × r:F p ∧ ¬q : F p:F × r:T × ¬q : F q:T × (j) Denote “Bonnie comes/will come to the party” by p, “Clyde comes/will come to the party” by q , and “Alice comes/will come to the party” by r Then the argument is based on the following inference rule: ¬p → (¬q ∨ r ), q → ¬r q→p