Homework SourseAnswer the question use truth tables Does implication distri
Answer the question use truth tables
Does implication distribute over conjunction from the right, left, both, or neither?
This is my modern class. Don\'t understand what\'s it asking. I think it\'s to do with propositional arguments.
Solution
its a left
| Line | Pool | Formula | Rule | Depends upon | Notes | |
|---|---|---|---|---|---|---|
| 1 | 1 | p(qr) | Assumption | (None) | ||
| 2 | 2 | p | Assumption | (None) | ||
| 3 | 1, 2 | qr | Modus Ponendo Ponens: E | 1, 2 | ||
| 4 | 2 | p | Law of Identity | 2 | ||
| 5 | 5 | q | Assumption | (None) | ||
| 6 | 5 | pq | Rule of Implication: I | 4 – 5 | Assumption 4 has been discharged | |
| 7 | 5 | (pq)(pr) | Rule of Addition: I1 | 6 | ||
| 8 | 8 | r | Assumption | (None) | ||
| 9 | 8 | pr | Sequent Introduction | 8 | True Statement is implied by Every Statement | |
| 10 | 8 | (pq)(pr) | Rule of Addition: I2 | 9 | ||
| 11 | 1 | (pq)(pr) | Proof by Cases: PBC | 3, 2 – 7, 8 – 10 | Assumptions 2 and 8 have been discharged |
