Over on Math.stackexchange I was discussing probability jargon. Typically the events considered in probability theory are constructed from other, simpler events by a series of unions, intersections, and complements, which have the following meanings:
Complement of event A: "Event A does not happen"
Intersection of events A and B: "Events A and B both happen"
Union of events A and B: "At least one of the events A, B happens"
The existing jargon to describe these is imperfect for events. Although opposite for complement and coincidence for intersection work well, I had trouble finding a good event-based name for union:
The union of two events, though, is harder to come up with a good informal name for. Terms like umbrella, compass, ambit, scope, range, orbit, menu which describe a list of possible selections sound weird when phrased as events that happen: "the umbrella of A or B happens if..." I thought of terms like participation, intervention, intrusion, inclusion, but these all have (literally) unwanted overtones and/or make the events sound personified in a weird way. Occurrence and instance sound better to describe "at least one of these events happens" but have the drawback that they apply to single events; there's no necessary reason for them to apply to a union of multiple events. Concurrence sounds like another description for intersection, as does conjunction, which is too jargony. Disjunction is also too jargony and sounds like "A or B but not both". Option and choice imply that someone in particular is picking which event happens.
The least-bad idea that I came up with for union is alternative: the alternative of A or B happens iff at least one of A, B happens. Could not be used as a verb ("A or B alternate"??) but implies two or more possibilities without also implying that someone is picking which event happens, or that the events are like people "participating" or "intruding". Does anyone have a better one?
So I put it to you: what's a relatively informal, single-word English expression for "the event where at least one of this group of events takes place?"