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Taxonomy is indispensable in understanding natural language. A variety of large scale, usage-based, data-driven lexical taxonomies have been constructed in recent years.Hypernym-hyponym relationship, which is considered as the backbone of lexical taxonomies can not only be used to categorize the data but also enables generalization. In particular, we focus on one of the most prominent properties of the hypernym-hyponym relationship, namely, transitivity, which has a significant implication for many applications. We show that, unlike human crafted ontologies and taxonomies, transitivity does not always hold in data-drivenlexical taxonomies. We introduce a supervised approach to detect whether transitivity holds for any given pair of hypernym-hyponym relationships. Besides solving the inferencing problem, we also use the transitivity to derive new hypernym-hyponym relationships for data-driven lexical taxonomies. We conduct extensive experiments to show the effectiveness of our approach.