SOLUTION: I cannot solve this: I can use: Transportation, Material Implication, Material Equivalence, Exportation, Tautology, Double Negation, Commutation, Association, Distribution, Demorga

Question 188807: I cannot solve this: I can use: Transportation, Material Implication, Material Equivalence, Exportation, Tautology, Double Negation, Commutation, Association, Distribution, Demorgan's Theorem, Modus Ponems, Modus Tollens, Hypothetical Syllogism, Conjunstion, Simplification, Addition, Constructive Dilemma, Absorption and Disjuntive Syllogism.
6. 1. (p v q) -> r
2. r -> (s <--> t)
3. s -> ~t Therefore: ~p v ~t
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1. (p v q) -> r
2. r -> (s <--> t)
3. s -> ~t Therefore: ~p v ~t
-------------------------------
4.  r -> [ (s -> t) & (t -> s) ]                      2  Material Equivalence 
5.  ~r v [ (s -> t) & (t -> s) ]                      4  Material Implication
6.  [~r v (s -> t)] & [~r v (t -> s)]                 5  Distribution
7.  [~r v (t -> s)] & [~r v (s -> t)]                 6  Commutation
8.  ~r v (t -> s)                                     7  Simplification
9.  r -> (t -> s)                                     8  Material Implication
10. (r & t) -> s                                      9  Exportation
11. (r & t) -> ~t                                  3,10  Hypothetical Syllogism
12. r -> (t -> ~t)                                   11  Exportation
13. r -> (~t v ~t)                                   12  Material Implication 
14. r -> ~t                                          13  Tautology
15. (p v q) -> ~t                                  1,14  Hypothetical Syllogism
16. ~(p v q) v ~t                                    15  Material Implication
17. (~p & ~q) v ~t                                   16  DeMorgan's Theorem
18. ~t v (~p & ~q)                                   17  Commutation
19. (~t v ~p) & (~t v ~q)                            18  Distribution
20. ~t v ~p                                          19  Simplification
21. ~p v ~t                                          20  Commutation

RELATED QUESTIONS
I cannot solve this: I can use: Transportation, Material Implication, Material... (answered by jim_thompson5910)

I cannot solve this: I can use: Transportation, Material Implication, Material... (answered by jim_thompson5910)

I can use: Transportation, Material Implication, Material Equivalence, Exportation,... (answered by jim_thompson5910)

I need to solve using Transportation, Material Implication, Material Equivalence,... (answered by jim_thompson5910)

Here is a proof that I have been unable to solve. I can solve it using Indirect Proof... (answered by richard1234)

I�m doing homework concerning the rules of replacement. We are allowed to use 8 rules of... (answered by jim_thompson5910)