] >
I will use the same table as in ponderable 1.1.1. Now, there are three variables, each can be T or F, so the table needs 23=8 rows. We must verify that the third ⇒ column is filled with T.
((p | ⇒ | q) | ∧ | (q | ⇒ | r)) | ⇒ | (p | ⇒ | r) |
---|---|---|---|---|---|---|---|---|---|---|
T | T | T | T | T | T | T | T | T | T | T |
T | T | T | F | T | F | F | T | T | F | F |
T | F | F | F | F | T | T | T | T | T | T |
T | F | F | F | F | T | F | T | T | F | F |
F | T | T | T | T | T | T | T | F | T | T |
F | T | T | F | T | F | F | T | F | T | F |
F | T | F | T | F | T | T | T | F | T | T |
F | T | F | T | F | T | F | T | F | T | F |
QED.