language proof and logic solutions chapter 6
∨ q) ∧ (¬p)" implies q. Solution: Assume "(p ∨ q) ∧ ¬p" (Premise) From conjunction, infer: p ∨ q (from 1) ¬p (from 1) Use disjunctive syllogism: Since p is false (¬p), and p ∨ q is true, then q must be true. Therefore, q is logically implied. Problem 2: Show that "p → (q → p)" is a tautology. Solut