Word for compound event: "At least one of these events will happen"

Question

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?"

Answer 1

A union really is the closest term for this, or a more extended "either one or both"; informal conversation is not as precise as a logician in its terms for abstract causes or events.

That said, if you wanted to coin another term, inclusive (adj., historically also n.) describes this function. Oxford English Dictionary, "inclusive, n. and adj.":

[adj.] 8. Chiefly Logic and Linguistics. Designating or relating to (the use of) a disjunction (esp. ‘or’) forming compound statements which are true if and only if at least one of the component statements is true (with the possibility that both are true). Cf. earlier sense A.

The adjective form is the one commonly included in logic and mathematics under the term inclusive or, describing an or statement that should include one, the other, or both events. (In common usage, or is often exclusive, indicating one or the other but not both.)

That said, its use as a noun or a substantive is not unknown, as sense A from the same entry attests:

A statement which is true if any one of a number of component statements it includes is true. Cf. sense B. 8, exclusive n. 1. Obsolete.

So you could add this to your list of least-bad ideas:

Winning this card game is inclusive of getting closest to 21 or the opponent going over 21?

the inclusive of A or B happens iff [if and only if] at least one of A, B happens.

Answer 2

I must say that while reading your explanation, at the point where you consider the first various possible terms, I said to myself "Why not use the term "alternative" (the alternative of A and B)?". It looks like the best option; however, it implies exclusion of one of the two and a verb "to alternate" does not mean "to occur as one of two possibility or jointly". The noun "concurrence" is general enough in its meaning, though.

(SOED) 2a Joint action, cooperation

Moreover, the verb "to concur" means (SOED)

"Act in concert, cooperate; Of causes, etc.: combine (to produce a result)".