Converse and equivalence
But the fact that some geniuses were laughed at does not imply that all who are laughed at are geniuses. They laughed at Columbus, they laughed at Fulton [steamboat inventor], they laughed at the Wright brothers. But they also laughed at Bozo the Clown.
Carl Sagan, Broca’s Brain, 1979
Statements of the form A B are at the heart of mathematics. We have seen that for an implication A B we can take its inverse (not( ...