Three experiments with preschool- and young school-aged children (N = 75 and 53) explored the kinds of relations children detect in samples of instances (descriptive problem) and how they generalize those relations to new instances (inferential problem). Each experiment initially presented a perfect biconditional relation between two features (e.g., all and only frogs are blue). Additional examples undermined one of the component conditional relations (not all frogs are blue) but supported another (only frogs are blue). Preschool-aged children did not distinguish (...) between supported and undermined relations. Older children did show the distinction, at least when the test instances were clearly drawn from the same population as the training instances. Results suggest that younger children’s difficulties may stem from the demands of using imperfect correlations for predictions. Older children seemed sensitive to the inferential problem of using samples to make predictions about populations. (shrink)