Contingent Wffs
Wffs which are neither tautologies nor contradictions are contingent. A contingent
wff is true on at least one row and false on at least one row. Let's look again at a
wff we tested in the last section:
We tested ((A v B) & (C ⊃ ~A)) to see whether it was a contradiction:
| A | B | C | (A v B) | ~A | (C ⊃ ~A) | ((A v B) & (C ⊃ ~A)) |
| T | T | T | T | F | F | F |
| T | T | F | T | F | T | T |
| T | F | T | T | F | F | F |
| T | F | F | T | F | T | T |
| F | T | T | T | T | T | T |
| F | T | F | T | T | T | T |
| F | F | T | F | T | T | F |
| F | F | F | F | T | T | F |
((A v B) & (C ⊃ ~A)) is not a contradiction, because it is true on at least one row of the truth table. It is not a tautology, because tautologies are true on all rows. So it is a contingency, since it is true on at least one row and false on at least one row.
Question: We noted that the negation of a tautology is a contradiction, that the negation of a contradiction is a tautology. What about the negation of a contingent wff?
Now that we've explained tautologies, contradictions and contingent wffs, you should be able to determine the logical status of any wff using the truth table method. Here's an exercise in doing exactly that.
 |
 |
| table of contents | List of Exercises |