The purpose of the study was to examine whether or not within-sets generalization (WSG) and between-sets generalization (BSG) are dependent on transitive stimulus generalization (TSG). A match-to-sample training procedure was used to train four typically developing five-year-old children to select stimuli from set A (fractions in ratio form) in the presence of stimuli from either set B or set C (fractions in picture form). The emergence of TSG, WSG, and BSG then was examined through presentations of stimuli involved in training and stimuli not involved in training.;Participants then were trained on the certain combinations of stimuli that were used to check for demonstrations of TSG. Demonstrations of TSG, WSG, and BSG then were examined after the TSG training in order to determine whether TSG training affected demonstrations of WSG or BSG. Participants then were trained on the certain combinations of stimuli that were used to check for demonstrations of WSG. Demonstrations of TSG, WSG, and BSG then were examined after the WSG training in order to determine whether WSG training affected demonstrations of BSG.;The data patterns of three of the four participants suggested that increased TSG training affected an increase in WSG responding, and the data pattern of only one of the four participants offered limited support that increased TSG training affected an increase in BSG responding. The data pattern of one of the four participants suggested that the addition of WSG training to TSG training affected an increase in BSG responding