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

Question 188805: 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.
4. 1. p <--> q
2. p -> r
3. p -> (r -> s) Therefore: q -> s

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1. p <--> q
2. p -> r
3. p -> (r -> s) Therefore: q -> s
------------------------------------
4.  (p -> q) & (q -> p)                      3     Material Equivalence
5.  (q -> p) & (p -> q)                      4     Commutation
6.  q -> p                                   5     Simplification
7.  q -> r                                   6,2   Hypothetical Syllogism
8.  q -> (r -> s)                            6,3   Hypothetical Syllogism
9.  (q & r) -> s                             8     Exportation
10. ~(q & r) v s                             9     Material Implication    
11. (~q v ~r) v s                            10    DeMorgan's Theorem
12. ~q v (~r v s)                            11    Association
13. ~q v (s v ~r)                            12    Commutation
14. (~q v s) v ~r                            13    Association
15. (q -> s) v ~r                            14    Material Implication
16. ~r v (q -> s)                            15    Commutation
17. r -> (q -> s)                            16    Material Implication
18. q -> (q -> s)                            7,17  Hypothetical Syllogism
19. (q & q) -> s                             18    Exportation
20. q -> s                                   19    Tautology

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