SOLUTION: How do you work through this problem? Use indirect proof: 1. ∼A ⊃ (B • C) 2. D ⊃ ∼C / D ⊃ A

Algebra ->  Proofs -> SOLUTION: How do you work through this problem? Use indirect proof: 1. ∼A ⊃ (B • C) 2. D ⊃ ∼C / D ⊃ A       Log On


   

Question 1157554: How do you work through this problem?
Use indirect proof:
1. ∼A ⊃ (B • C)
2. D ⊃ ∼C / D ⊃ A
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

1.	∼A ⊃ (B • C)	 
2.	D ⊃ ∼C	        / D ⊃ A

           | 3.  ~(D ⊃ A)      Assumption for Indirect Proof
           | 4.  ~(~D v A)     3, Material Implication
           | 5.  ~~D • ~A      4, DeMorgan's Law
           | 6.  D • ~A        5, Double Negation
           | 7.  D             6, Simplification
           | 8.  ~A • D        6, Commutation 
           | 9.  ~A            8, Simplification
           |10. ~C             2,7, Modus Ponens 
           |11. ~C v ~B        10, Addition
           |12. ~(C • B)       11, DeMorgan's Law
           |13. ~(B • C)       12, Commutation
           |12. ~~A            2,13, Transposition
           |13. A              12, Double Negation
           |14. A • ~A         13,9, Conjunction
15. D ⊃ A         Lines 3-14   Indirect Proof

Edwin