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Multiple instance learning (MIL) is a widely researched learning paradigm that allows a machine learning algorithm to learn target concepts from data with uncertain class labels. The random set framework for multiple instance learning (RSF-MIL) makes use of the random set to learn in this scenario of uncertainty. Previous models used assumptions that imposed a disjunctive relationship between the simple concepts learned (which compose the target concept). In the following, a conjunctive formulation of RSF-MIL is proposed and investigated. Results illustrate the utility of the conjunctive and disjunctive formulations of RSF-MIL and the scenarios when each is applicable.