Given a model of a system and an objective, the model-checking problem asks whether the model satisfies the objective. In this case, the model is a Markov Decision Process (MDP), and the objective is safety: given a set of target vertices $T\subseteq V$, determine whether there is an infinite path that does not visit any vertex in $T$ (i.e. you want to avoid all vertices in $T$). Furthermore, given $k$ safety objectives, the disjunctive safety query question asks whether there is a strategy for player 1 to ensure that one of the safety objectives is satisfied with probability 1. Disjunctive queries do not coincide with disjunctive objectives on MDPs.