SOLUTION: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument: 1. (A & U) < > ~R 2. ~(~R v ~A) / ~U

Algebra ->  Proofs -> SOLUTION: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument: 1. (A & U) < > ~R 2. ~(~R v ~A) / ~U      Log On


   

Question 1010731: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. (A & U) < > ~R
2. ~(~R v ~A)
/ ~U
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
 1. (A & U) < > ~R 
 2. ~(~R v ~A)         
    / ~U

 3. ~~R & ~~A                        2, DeMorgan's theorem
 4. R & A                            3, Double negation
 5. R                                4, Simplification
 6. [(A & U) > ~R] & [~R > (A & U)]  1, Material equivalence
 7. (A & U) > ~R                     6, Simplification
 8. ~~R > ~(A & U)                   7, Transposition
 9. R > ~(A & U)                     8, Double negation
10. ~(A & U)                         9,5 Modus ponens
11. ~A v ~U                          10, DeMorgan's theorem
12. A & R                            4, Commutation
13. A                                12, Simplification
14. ~~A                              13, Double negation
15. ~U                               11,14 Disjunctive syllogism    

Edwin