The history of distributed computing is full of trade-offs between safety and liveness. For instance, one of the most celebrated results in the field, namely the impossibility of consensus in an asynchronous system basically says that we cannot devise an algorithm that deterministically ensures consensus agreement and validity (i.e., safety) on the one hand, and consensus wait-freedom (i.e., liveness) on the other hand. The motivation of this work is to study the extent to which safety and liveness properties inherently exclude each other. More specifically, we ask, given any safety property S, whether we can determine the strongest (resp. weakest) liveness property that can (resp. cannot) be achieved with S. We show that, maybe surprisingly, the answers to these safety-liveness exclusion questions are in general negative. This has several ramifications in various distributed computing contexts. In the context of consensus for example, this means that it is impossible to determine the strongest (resp. the weakest) liveness property that can (resp. cannot) be ensured with linearizability. However, we present a way to circumvent these impossibilities and answer positively the safety-liveness question by considering a restricted form of liveness. We consider a definition that gathers generalized forms of obstruction-freedom and lock-freedom while enabling to determine the strongest (resp. weakest) liveness property that can (resp. cannot) be implemented in the context of consensus and transactional memory.