Word that means "one out of a series must be true"?

I am trying to come up with a word or phrase that means "one out of a series must be true".

Example #1:

I have a list of roles that a user can belong to. What is a word that describes a list of roles where the user may belong to one of them? They could belong to more than one.

Example #2:

There is a list of requirements to be eligible for a prize. You may meet multiple requirements, but you only need to meet one requirement to be eligible.

Sentence example: The following roles are _______.

The best that I can come up with is "required roles", but, that seems funky to me as not all of the roles are required.

The way I would generally address your first case is by looking at it one level of abstraction up: a role is required, and the role may be any one of the list of possible cases.

You could possibly say about your second case that each requirement is sufficient (as in the concepts of sufficiency and necessity in logic). Having a bunch of sufficient conditions implies that you have to have at least one of them, otherwise there are zero sufficient conditions and the statement fails.

I wouldn't use that term in user interface, but it may be helpful for internal nomenclature.

If the user can belong to only one, the roles are mutually exclusive because belonging to any one excludes membership of all the others.

I'm not entirely sure that "Mutually inclusive" describes roles the user must belong to; "compulsory roles" might be better.

In computer user interfaces, I think it's common to say "required field" for anything where the user must make SOME selection. This is most often applied to text entry, to indicate that you cannot leave it blank, but it also often used for multiple-choice lists.

If you're afraid of ambiguity, you could always say "Role (choose at least one)".

I can't think of a commonly-used word that means "you must select at least one from the following list". If someone else here thinks of such a word, I'll be happy to upvote you. :-) If there's an obscure word, it probably doesn't do you much good, as by definition that means most of your users wouldn't know what it means. I'd rather use four common words that people understand than one obscure word that no one understands.

I see a problem with OP's "sentence example" The following roles are ------, because that would imply the target word somehow describes each role. But what OP actually seeks is a word describing the list.

The first list is an exhaustive list, meaning that it contains all possible roles.

If it's only possible to choose one role from the list, it contains mutually exclusive options.

If it's necessary for every user to choose a role, this would normally be described as a mandatory or compulsory choice. But note that this description applies to the act of making a choice, not to the list as a whole, or any individual roles within it.

The second example is somewhat different - it's not actually mandatory that the user should meet any of the requirements (he just won't be eligible for a prize if he doesn't). I would describe this situation by saying he must meet at least one of the eligibility criteria to have a chance of winning.