Question 188933: 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.
1. p -> (q & r)
2. ~t -> (~r v ~s) Therefore: (p & s) -> t
I know that you must somehow get:
~p
~p v ~s Add
~(p & s) Demorgans
~(p & s) v t Addition
(p & s) -> t Implication OR
~t -> t
t v t Implication
t Tautology
t v ~(p & s) Addition
~(p & s) v t Commutation
(p & s) -> t Implication
But I cannot get the steps before these. Please help!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Note: try to involve every premise (the given lines) to find the conclusion.
1. p -> (q & r)
2. ~t -> (~r v ~s) Therefore: (p & s) -> t
----------------------------------------------
3. ~~t v (~r v ~s) 2 Material Implication
4. t v (~r v ~s) 3 Double Negation
5. (~r v ~s) v t 4 Commutation
6. ~r v (~s v t) 5 Association
7. ~r v (s -> t) 6 Material Implication
8. r -> (s -> t) 7 Material Implication
9. ~p v (q & r) 1 Material Implication
10. (~p v q) & (~p v r) 9 Distribution
11. (~p v r) & (~p v q) 10 Commutation
12. ~p v r 11 Simplification
13. p -> r 12 Material Implication
14. p -> (s -> t) 13,8 Hypothetical Syllogism
15. (p & s) -> t 14 Exportation
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