One experiment tested the effects of systematically negating the constituents of four fundamental inferences based on conditionals: Modus Ponens (i.e. inferences of the form: if p then q; p therefore q), Modus Tollens (if p then q; not‐q therefore not‐p); Affirmation of the Consequent if p then q; q therefore p), and Denial of the Antecedent (if p then q; not‐p therefore not‐q). The latter two inferences are valid only for bi‐conditionals (if, and only if, p then q). The participants drew their own conclusions from premises about letters and numbers on cards. We observed a significant effect of explicit negatives on Modus Tollens and Denial of the Antecedent problems: The inferences were drawn more often for conditionals that yield a negative conclusion (e.g. if p then not q; q therefore not p) than for conditionals that yield an affirmative conclusion (e.g. if not p then q; not‐q therefore p). Additionally, we observed a similar, but smaller effect on Affirmation of the Consequent problems. Furthermore, we observed a significant effect of the categorical premise (affirmative or negative), especially on Affirmation of the Consequent problems. Finally, we observed an effect of the magnitude of the contrast class. If the contrast is larger (a set of three, five or nine values), then the making of a double negation or the production of an affirmative conclusion is more difficult for Denial of the Antecedent inferences. We discussed the results in relation to a negative categorical premise bias, an affirmative premise bias, a negative conclusion bias and a double negation effect.