Abstract : In a Software Product Line (SPL) comprising specifications (feature sets), implementations (component sets) and traceability between them, the definition of product is quite subtle. Intuitively, a strong relation of implementability should be established between implementations and specifications due to traceability. Various notions of traceability has been proposed in the literature : , , , ; but we found in our experience that they do not capture all situations that arise in practice. One example is the case where, an implementation, due to packaging reasons, contains additional components not required for a particular product specification. We have defined a general notion of traceability in order to cover such situations. Moreover, state-of-the-art satisfiability based notions lead to products where the implementability relation does not exist. Therefore, in this paper, we propose a simple, set-theoretic formalism to express the notions of traceability and implementability in a formal manner. The subsequent definition of SPL products is used to introduce a set of analysis problems that are either refinements of known problems, or are completely novel. Last but not the least, we propose encoding the analysis problems as Quantified Boolean Formula (QBF) constraints and use Quantified SAT (QSAT) solvers to solve these problems efficiently. To the best of our knowledge, the QBF encoding is novel; we prove the correctness of our encoding and demonstrate its practical feasibility through our prototype implementation Software Product Line Engine (SPLE).