A logical error that people make. In general if A then B does not mean if B then A. It sometimes does, in which case it is said if and only if A then B. For example, it is true to say that "If you are a horse, then you are an animal". But this does not necessarily lead to the converse: "If you are an animal, then you are a horse". This is an example of a converse error.

Usually, the above is fairly easily to explain, and people accept it if you correct them. But it gets confusing if you use the contrapositive form of the statement. The contrapositive of "if A then B" is not "if not A then not B", but actually "if not B then not A". For example. let's go back to animals and horses. The negation of "If you are a horse then you are an animal" is NOT "If you are not a horse, then you are not an animal", but "if you are not an animal, then you are not a horse".

For example, here's an argument that make a converse error based on the contrapositve.: If you get slashed with a knife, then you start to bleed; I wasn't slashed with a knife, therefore I mustn't be bleeding.

Here's a joke that's built on converse error combined with the contrapositive.

Descartes walks into a bar. The barman says "Fancy a beer?" Descartes says "I think not!" and disappears.