Children's language and world knowledge grows explosively in the preschool years. One critical contributor to this growth is their developing ability to infer relations beyond those that have been directly taught or modeled. Categorization is one type of skill commonly taught in preschool in which inference is an important aspect. This study explored the development of specific types of inferences within a categorization relation: those among naming items and categories, selecting items based on their names and categories, and answering questions that relate names and categories. Children learned names and categories for a set of unfamiliar cartoon characters through one of two training protocols: (a) Listener training involved selecting a picture upon hearing an item name or category; (b) Expressive training involved saying an item name or category upon seeing a picture. Following training, we tested whether children derived several kinds of untrained responses. Those children who received Expressive training (saying names) completed tests of listener responses (selecting pictures); similarly, those children who received Listener training (selecting pictures) completed tests of expressive responses (saying names). Next, children answered oral questions in the absence of pictures. Results show that children receiving Expressive and Listener training produce naming and question answering responses at levels above chance. However, many children failed to answer all questions correctly. The Expressive group produced naming and question answering responses at significantly higher levels than the Listener group. This suggests that Listener training is a weaker form of instruction when the goal of instruction is the production of untrained responses. However, these results are tentative because unequal proportions of children completed each type of training. Finally, we examined the relationship between naming and question answering. Few children answered questions at a higher level than they produced names. This study shows that children learn to infer responses from both Listener and Expressive trainings. This study also suggests that naming and question answering responses are related responses. The current study highlights the need for later research on teaching inference skills such as naming and question answering to those who do not develop them in the absence of specific instruction.