What is a 'disjunct' of a union called? Say I have a set $C = A \cup B$ and I want to refer to $A$ in natural language. Had the expression been a Boolean formula with a disjunction, then I would call $A$ the first disjunct. 
Is there a similar term when speaking about unions?
The context is the following. I have a set $C$ defined as the union of two unnamed sets with long descriptions: $C = \{a \in U : \dots \} \cup \{b \in U : \dots \}$. After the definition of $C$, I would like to clarify the role of each of the two sets, using a sentence like
The first ??? ensures that $C$ ... while the second ??? guarantees that $C$ is ...
As the description for each set is long, and space scares, I cannot refer to them by that. I am not interested in wasting space introducing names for the sets, as they are referred to directly only once.
 A: Since we are describing $C$ as the union of two sets, why not simply refer to $A$ as the first set in this union of two sets.
But, honestly, I'd simply refer to these sets by name. If you state that $C = A\cup B$, why not go on to assert:  
"Set $A$ ensures...., while $B$ guarantees..."
A: To summarize all of the suggestions, as of writing this:

*

*Set

*Term

*Use the explicit name introduced earlier

*Unionand

*Unionee

*Component (only suggested for disjoint unions)


My personal thoughts and feelings: I want a good, distinct term for this.  Because I often want to have a nice, sing-songy, catchy expression for countable additivity.  For instance, something like "The measure of the union is the sum of the measures of the ..."  I want to delay introducing symbols and try to give a more natural-language expression if I possibly can.
I would suggest "unit" for one term/set in a union, suggesting that it is what "exists" before it is united with other terms/sets.  Unfortunately mathematicians use "unit" a bit too much for other concepts, so I don't think this is the best route.
I don't want something that sounds so confusing as "unionand", especially when I suspect that its analog "summand" comes from some rule of Latin and "unionand" probably doesn't conform to the same rule.
In other contexts, we talk about a "union" between man and wife, or between states.  But I think we'd all find it really weird to call a term/set a "spouse" or "ally".

How about we just bite the bullet and use something silly and fun?  Like a "uny".
Each little uny in the union.  :)
