SOLUTION: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument: 1. C 2. (C & T) > ~T 3. (C & ~T) > T / T < > ~T

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Question 1010733: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. C
2. (C & T) > ~T
3. (C & ~T) > T / T < > ~T
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

 1. C 
 2. (C & T) > ~T 
 3. (C & ~T) > T / T < > ~T

 4. ~~T > ~(C & T)      2, Transposition
 5. T > ~(C & T)        4, Double negation
 6. T > (~C v ~T)       5, DeMorgan
 7. ~T v (~C v ~T)      6, Material Implication
 8. ~T v (~T v ~C)      7, Commutation
 9. (~T v ~T) v ~C      8, Association
10. ~T v ~C             9, Tautology
11. ~C v ~T            10, Commutation
12. ~~C                 1, Double Negation
13. ~T                 11,12, Disjunctive Syllogism
14. C & ~T              1,13, Conjunction
15. T                   3,14, Modus Ponens
16. T v T               15, Addition
17. ~~T v T             16, Double Negation
18. ~T > T              17, Material Implication
19. ~T v ~T             13, Addition
20. T > ~T              19, Material Implication
21. T < > ~T            20,18, Material Equivalence

Edwin