Impulse differential inclusions provide a framework for modelling hybrid phenomena. In the context of impulse differential inclusions, verification for safety specifications and safe controller synthesis can be formulated as viability and invariance questions for appropriate sets of states. In this paper, a characterisation of viability and invariance kernels (i.e. the largest subsets of a given set that are viable or invariant) is presented. In the process, a method for computing these sets using standard viability and invariance tools is developed.