Modus tollens

We also can work with negations to create a valid argument:

$ $$\begin{array}{c}\text{If Socrates is a fish, then Socrates can live underwater.}\text{Socrates cannot live underwater.}\\ hline\text{Therefore, Socrates is not a fish.}\end{array}$$ $

Also known as law of contrapositive or denying the consequent, modus tollens works by reversing modus ponens. Formally,

$ $$\begin{array}{c}A\to B\neg B\\ hline\therefore \neg A\end{array}$$ $