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

Question 188809: 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.
8. 1. p -> (q -> r)
2. ~ (q & ~r) -> s
3. s -> t
4. t <--> (q & ~s) Therefore: p <--> s
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!


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

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