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