P q r q p r ∴ q aka Disjunction Elimination Corresponding Tautology ((p q) ∧ (r q) ∧ (p r )) q Example Let p be "I will study discrete math" Let q be "I will study Computer Science" Let r be "I will study databases" "If I will study discrete math, then I will study Computer Science" 2 P → Q A s s u m This second assumption is good too, since you basically want to do a DeMorgan on line 1, and to do those in Natural Deduction, you do a Proof by COntradiction on each of the disjuncts so yes, assume the disjunct, but then proceed with getting the full disjunct 3 ( P → Q) ∨ ( Q → P) ∨ I n t r o ( 2) and now youRule of inference of type PC says that if set B= {p1, p2,, pn} and p is propositional consequence of set B, then p1^p2^^pn→p is tautology Then in this case (B, p) is an order pairs or rule of inference of type PC For your case, let Set B'= {p→q, p} and we know that q is propositional consequence of set B' because p→q^p→q is a tautology
Simplify Combining Like Terms P P Q Q Q Q P
Divide: p - q p + q p - q