Formal Fallacies

Reverse Chain

If P, then Q. If Q, then R. Therefore, if R, then P.

The symbolic form looks like this;

The reason this is a fallacy is the same reason that affirming the consequent is a fallacy. It does not follow that if the necessary condition of one premise is present that the sufficient condition of another will be. This is working backwards.

Example:
If it is raining, then it is cloudy. If it is cloudy, then I'll be sad. Therefore, if I am sad, then it is raining. This incorrectly assumes that the only possible reason for sadness is rain. We know there are other causes of sadness. Rain is just one of them (for this person).