SOLUTION: Hi, I need help with finishing these proofs for my PHI class I am so confused! :( [1] 1. ~T 2. R ⊃S 3. S⊃T Conclusion: /~R [2] 1. (F · P)⊃~Y 2

Algebra ->  Proofs -> SOLUTION: Hi, I need help with finishing these proofs for my PHI class I am so confused! :( [1] 1. ~T 2. R ⊃S 3. S⊃T Conclusion: /~R [2] 1. (F · P)⊃~Y 2      Log On


   



Question 999025: Hi, I need help with finishing these proofs for my PHI class I am so confused! :(
[1]
1. ~T
2. R ⊃S
3. S⊃T Conclusion: /~R

[2]
1. (F · P)⊃~Y
2. F
3. J⊃Y
4. P Conclusion: /~J

[3]
1. A v (Bv D)
2. ~A
3. B⊃X
4. D⊃~H
5. ~X Conclusion: /~H

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
1. ~T
2. R ⊃ S
3. S ⊃ T     Conclusion: /~R 

4. ~T ⊃ ~S         3. Transposition
5. ~S              4. Modus ponens    
6. ~S ⊃ ~R         5. Transposition
7. ~R              6,5, Modus ponens

It's easier if you think of them like this, because
they become common sense:

Modus ponens:

If you know that the first implies the second,
then if you have the first, you MUST have the second.

Transposition:  

If the first implies the second, then if you don't have
the second then you MUST NOT have had the first.

---------------------------
1. (F · P) ⊃ ~Y
2. F
3. J ⊃ Y
4. P       Conclusion: /~J 

5. F · P           2,4, Conjunction of premises  
6. ~Y              1,5, Modus ponens
7. ~Y ⊃ ~J           3, Transposition
  
Conjunction of premises:

If you know the first and you know the second,
then you know the first and the second.


---------------------------
 1. A v (B v D)
 2. ~A 
 3. B ⊃ X
 4. D ⊃ ~H
 5. ~X          Conclusion: /~H

 6. ~X ⊃ ~B          3, transposition.
 7. ~B             6,5, modus ponens  
 8. B v D          1,2, disjunctive syllogism
 9. D              8,7, disjunctive syllogism
10. ~H             4,9, modus ponens 



Think of disjunctive syllogism this way:

If you know that you have either the first or the second, 
then if you don't have the first, you MUST have the second.

Edwin