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
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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
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