SOLUTION: Formal proof: In the text box below, use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid: (A • B) ⊃ (E ⊃ A), (A •

Algebra ->  Proofs -> SOLUTION: Formal proof: In the text box below, use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid: (A • B) ⊃ (E ⊃ A), (A •       Log On


   

Question 1188425: Formal proof: In the text box below, use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
(A • B) ⊃ (E ⊃ A), (A • B) v C, C ⊃ D /.: (E ⊃ A) v D
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 1. (A • B) ⊃ (E ⊃ A)
 2. (A • B) v C
 3. C ⊃ D                /.: (E ⊃ A) v D

                  |4. ~[(E ⊃ A) v D]         Assumption for Indirect Proof
                  |5. ~(E ⊃ A) • ~D                     4, DeMorgan's law   
                  |6. ~D • ~(E ⊃ A)                     5, Commutation
                  |7. ~D                                6, Simpliofication
                  |8. ~C                                3,8, Modus Tollens    
                  |9. C v (A • B)                       2, Commutation
                 |10. A • B                             9,8, Disjunctive syllogism 
                 |11. E ⊃ A                            1,10, Modus ponens
                 |12. (E ⊃ A) v D                       11, Addition
                 |13. [(E ⊃ A) v D] • ~[(E ⊃ A) v D]   12,4, Conjunction            
14. E ⊃ A) v D        Lines 4-13              Indirect Proof

Edwin