We present a study of Romanian-speaking children's derivation of exclusivity implicatures from disjunctive utterances (e.g., 'The hen pushed the train or the boat', implying 'The hen didn't push both'). Specifically, we investigate the role that relevance plays in the absence of the stronger conjunctive alternative. We used a Truth Value Judgment Task in which disjunctive sentences were presented as answers to a question that made exclusivity relevant, but without explicitly mentioning the conjunctive alternative. We tested three forms of disjunction: prosodically marked sau 'or', and the complex sau…sau and fie…fie 'either or'. The results indicate that presenting an explicit QUD that does not contain the conjunctive alternative does not boost exclusivity: children interpreted all disjunctions inclusively. Our results suggest that relevance alone does not enhance exclusivity inferences and, taken together with results in Bleotu et al. (2024), support an 'Alternatives & QUD' account, on which both relevance and explicit alternatives are necessary.