A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 7.7, 2, p. 390

 Prove the logical truth.

 

1.     ~ [(~P ⊃ Q) v (P ⊃ R)] 2.     ~ (~P ⊃ Q) • ~ (P ⊃ R) 3.     ~ (P v Q) • ~ (~ P v R) 4.     ~ P • ~ Q • P • ~ R 5.     ~ P • P • ~ Q • ~ R 6.     ~ P • P 7.     ~ ~ [(~P ⊃ Q) v (P ⊃ R)] 8.     (~P ⊃ Q) v (P ⊃ R)

/ (~P ⊃ Q) v (P ⊃ R) AIP 1 DM 2 Impl 3 DM 4 Com 5 Simp 1-6 IP 7 DN