Rules of inference allow us to take two or more true inputs (sometimes called premises) and output a new statement which must be true as a consequence of the inputs. Unlike replacement rules, rules of inference allow us to reach new conclusions and learn something we did not know before.

This lecture starts our unit on rules of inference with modus ponens. Modus ponens says that if P implies Q is true and P is true as well, then Q must follow as a result.

For example, suppose

“If I am in California, I am in America.”

and

“I am in California.”

Then it must be true that you are in America.