Now suppose that the animal turns out to have a duck bill: then it must be a mammal (in this case a platypus).

On the other hand, if it is not a mammal, then it cannot have a duck bill.

Now consider the set of animals that either are not mammals, or have duck bills.

This is the set "(not **B**) or **A**"

\[ = \left( \lnot B \right) \cup A\]

\[ = B \rightarrow A.\]

Now suppose that the animal is indeed a mammal: then it must have a duck bill.

On the other hand, suppose the animal does not have a duck bill: then it cannot be a mammal.