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
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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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