| Problem 1. |
| Premise |
|
1 |
|
Iab&Sbc |
| Premise |
|
2 |
|
(^x)(Sac>Z) |
| 1 &E |
|
3 |
|
Iab |
| 1 &E |
|
4 |
|
Sbc |
| 3 I2 |
|
5 |
|
Iba |
| 4,5 I4 |
|
6 |
|
Sac |
| 2 ^E |
|
7 |
|
Sac>Z |
| 6,7 >E |
|
8 |
|
Z |
|
| Problem 2. |
| Assumption |
|
1 |
|
....what if |
Iab |
| 1 I2 |
|
2 |
|
....then... |
Iba |
| 1-2 >I |
|
3 |
|
Iab>Iba |
|
| Assumption |
|
4 |
|
....what if |
Iba |
| 4 I2 |
|
5 |
|
....then... |
Iab |
| 4-5 >I |
|
6 |
|
Iba>Iab |
|
| 3,6 =I |
|
7 |
|
Iab=Iba |
|
| 7 ^I |
|
8 |
|
(^y)(Iay=Iya) |
|
|
| Problem 4. |
| Premise |
|
1 |
|
Iab&Iba |
| 1 &E |
|
2 |
|
Iab |
| |
|
3 |
|
|
| |
|
4 |
|
|
| |
|
5 |
|
|
| |
|
6 |
|
|
| ~~~~ |
|
7 |
|
~ part II ~ |
| Premise |
|
8 |
|
Iab |
| 8 I2 |
|
9 |
|
Iba |
| |
|
10 |
|
|
| |
|
11 |
|
|
| 8,9 &I |
|
12 |
|
Iab&Iba |
|