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
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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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