Conjecturing is crucial to mathematics and an activity in which it is believed mathematics learners of all ages should engage. It has been found that mathematicians productively generate examples when they are formulating conjectures. In this paper we explore whether this is also the case for undergraduate non-specialist mathematics students by means of an instrumental case study. We label conjecturing tasks as either explicit or implicit to distinguish between tasks which explicitly ask students to make a conjecture and those in which conjecturing is evoked implicitly, and we discuss the benefit of Comprehensive Example Generation (by which an example set is generated sequentially and systematically) in the context of such conjecturing tasks. The consequences of using a digital environment for such tasks are also discussed.