I have a set of related data/objects for which, when undergoing some algorithm, there should be only one valid match. Is there a unique term for this type of set?A common practical use case would be a list displayed for user selection, or a list of keys that should have a single corresponding entry in a database table.To illustrate this, here are a few examples:[True, False]  (boolean)[Forward, Neutral, Reverse] (state machine status)[Rare, Medium, Well] (user preference)[Credit, Debit] (reference type)In each of these cases, only one element in the set will be contextually valid, where the context may be a database record, an instance of an object in memory, or a question on a survey.  Examples of sets that wouldn't meet this criteria:[Garage, Kitchen, Bedroom, Bathroom] (rooms in a home)[Email, Phone, Text] (method of communication)[All Countries in Europe] (places I visited)In these cases, the set is used as a bucket from which a selection may be made - but the selection is not necessarily expected to be a single item in the set.
What is the term for this set
terminology;sets
None of your examples holds up: each has queries that allow multiple answers, and each has queries that allow only singleton answers.So you are really after a property of queries.On the most abstract level, given a set $S$ the term you are looking for is function:$\qquad f : Q \to S \\\qquad f(q) = s \text{ s.t. } q(s) = 1$where $Q$ is the set of queries (predicates), i.e. $Q \subseteq S \to \{0,1\}$. Note how $f$ is a (well-defined) function if and only if all $q \in Q$ have a support (set of values on which $q$ is $1$) of size $1$.If queries end up being true for (i.e. returning) multiple values, we call $f$ a relation. Or, alternatively, a function that maps queries to (possibly empty) sequences of results, i.e.$\qquad f : Q \to S^*$.