Conditional (if-then)
Any two propositions P and Q can be joined by a conditional operator, producing the new, complex, proposition:
If P then Q
The proposition If P then Q is true if and only if either P is false or Q is true. It is false only when P is true and Q is false.
Truth Table
| P | Q | If P then Q |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Commentary
A special conditional occurs if we flip the P and Q around: we get if Q then P, which is the same as saying P only if Q.