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
