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Database users can be frustrated by having an empty answer to a query. In this paper, we propose a framework to systematically relax queries involving joins and selections. When considering relaxing a query condition, intuitively one seeks the \'minimal\' amount of relaxation that yields an answer. We first characterize the types of answers that we return to relaxed queries. We then propose a lattice based framework in order to aid query relaxation. Nodes in the lattice correspond to different ways to relax queries. We characterize the properties of relaxation at each node and present algorithms to compute the corresponding answer. We then discuss how to traverse this lattice in a way that a non-empty query answer is obtained with the minimum amount of query condition relaxation. We implemented this framework and we present our results of a thorough performance evaluation using real and synthetic data. Our results indicate the practical utility of our framework.