SOLUTION: Complete the following natural deduction proof. Thank you! 1. (R • J) ⊃ U 2. ~(~R • ~N) 3. J / U v N

Algebra ->  Proofs -> SOLUTION: Complete the following natural deduction proof. Thank you! 1. (R • J) ⊃ U 2. ~(~R • ~N) 3. J / U v N       Log On


   

Question 1029579: Complete the following natural deduction proof. Thank you!
1. (R • J) ⊃ U
2. ~(~R • ~N)
3. J
/ U v N
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. (R • J) ⊃ U----------------Hypothesis
2. (J • R) ⊃ U----------------Commutativity
3. J ⊃ ( R ⊃ U) --------------Exportation
4. J ---------------------Hypothesis
5. R ⊃ U --------------------Modus ponens on #3 and #4
6. ~(~R • ~N) -----------------Hypothesis
7. R v N ---------------------de Morgan's law and double negation
8. ~~R v N --------------------double negation
9. ~R ⊃ N -------------------Material implication
10. ~N ⊃ R -------------------Contrapositive of #9
11. ~N ⊃ U ------------------Hypothetical syllogism on #5 and # 10
12. ~~N v U ------------------Material implication
13. N v U ---------------------Double negation
14. U v N --------------------Commutativity