| Modus Ponens:
| |
| If p, then q. | |
| p. | |
| q. | |
| Example: | |
| If there is no God, then life is meaningless. | |
| There is no God. | |
| Life is meaningless. | |
| Modus Tollens: | |
| If p, then q. | |
| It is not the case that q. | |
| It is not the case that p. | |
| Example: | |
| If an all powerful and all merciful God exists, then there is no evil in the world. | |
| It is not the case that there is no evil in the world. | |
| It is not the case that an all powerful and all merciful God exists. | |