The realization of logic operations within passive crossbar memory arrays is a promising approach to expand the fields of application of such architectures. Material implication was recently suggested as the basic function of memristive crossbar junctions, and single bipolar resistive switches (BRS) as well as complementary resistive switches (CRS) were shown to be capable of realizing this logical functionality. Based on a systematic analysis of the Boolean functions, we demonstrate here that 14 of 16 Boolean functions can be realized with a single BRS or CRS cell in at most three sequential cycles. Since the read-out step is independent of the logic operation steps, the result of the logic operation is directly stored to memory, making logic-in-memory applications feasible.