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Primary users (PU) separation concerns with the issues of distinguishing and characterizing primary users in cognitive radio (CR) networks. We argue the need for PU separation in the context of collaborative spectrum sensing and monitor selection. In this paper, we model the observations of monitors as boolean OR mixtures of underlying binary latency sources for PUs, and devise a novel binary inference algorithm for PU separation. Simulation results show that without prior knowledge regarding PUs activities, the algorithm achieves high inference accuracy. An interesting implication of the proposed algorithm is the ability to represent n independent binary sources via (correlated) binary vectors of logarithmic length.