"Would you rather listen to my great talk or be sitting doing some boring analyses in your office?" This invitation sentence is an example of an informal fallacy, often found in politics or advertising, called the false dilemma or false dichotomy. This fallacy consists in reducing many options to only two dichotomous ones, hence forcing a choice between them. In my talk, I will discuss a specific variant of the false dilemma, that is, inferences from an incompatibility statement, like "Being in Torino is incompatible with being in Leuven". The two propositions are presented as contradictories (the propositions seem to have opposite truth values), while in fact they are contraries, that is, the propositions could be simultaneously false. Therefore, when two propositions are incompatible, the truth of one necessarily leads to the falsity of the other (if I'm in Torino, I'm not in Leuven), but critically, the falsity of one does not necessarily lead to the truth of the other (if I'm not in Torino, I'm not necessarily in Leuven). Based on a long trend of research on content-related variability in conditional reasoning, the predictions were that content would have an impact on how people reason with these incompatibility inferences. I will present a series of studies, with both adults and children as participants, which show that the tendency to fall into the false dilemma fallacy is indeed modulated by the background knowledge of the (adult and child) reasoner. These results provide additional evidence on the link between semantic information retrieval and deduction. (Joint work with Bojan Nys and Janie Brisson.)