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Abstract: This article starts off the observation that in certain cases, presuppositions triggered by an element inside a question nucleus may fail to project. In fact, in what looks like coordinated structures involving polar questions, presupposition projection patterns are exactly parallel to what is observed when the corresponding assertions are coordinated. The article further shows that these facts do not fall out straightforwardly from existing theories of polar questions, (apparent) coordinations of questions, and presupposition projection. Finally, it proposes a trivalent extension of inquisitive semantics such that the observed pattern can be understood in terms of existing theories of presupposition projection. The proposal has the following properties: (a) apparent coordinations of questions actually are coordinations of questions and (b) the semantic denotation of polar questions is asymmetric with respect to the “yes” and “no” answers.