Modus tollens

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

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

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

$ $$\begin{array}{l} A \rightarrow B \ \neg B \\hline \therefore \neg A \end{array}$$ $