# Is there a name for the operands of union and intersection?

For subtraction, in $$a - b$$, we call $$a$$ the minuend and $$b$$ the subtrahend. With logical conjunction, $$p \wedge q$$, we can call $$p$$ and $$q$$ the conjuncts.

Are there terms like this for the operands of set union? Is there a term for $$P$$ and $$Q$$ in $$P \cup Q$$?

Likewise, are there terms for the operands of an intersection?

The word subtract comes from the Latin verb subtrahō, whose conjugation gives subtrahendus as the future passive participle ('which is to be removed'), and thereby subtrahend in English. The English word minuend is likewise derived from the future passive participle (minuendus, 'which is to be made smaller') of minuō. Similar derivations include:

• integrō > integrandus > integrand
• sūmō > sūmendus > summand
• multiplicō > multiplicandus > multiplicand

So following the same derivation:

• The word intersect coming from Latin verb intersecō, whose future passive participle is intersecendus, leading to intersecend (or more likely intersecand, to give a hard 'c').
• The word union comes from the Latin verb uniō, whose future passive participle is ūniendus, leading to uniend (or perhaps uniand).

That said, I have never seen the words intersecand or uniend, so using them will probably cause more confusion than it is worth.

...in fact, prior to reading your question, I had never heard the words minuend or subtrahend, either.

How about "disjuncts" for $$p \vee q$$. And then just "conjuncts" and "disjuncts" again for $$P \cap Q$$ and $$P \cup Q$$ respectively (since those set theoretic operations are defined by applications of "and" and "or"). Sounds good to me, at least, although I've never even heard of "conjuncts".

• Maybe it's because I'm thinking in German, but to me "disjuncts" sounds like it suggests the sets to be disjoint. – Mars Plastic Jul 8 '19 at 20:11
• Just so you know I'm not making that up: Wikipedia uses both conjunct and disjunct. The Wikipedia site for conjunction has, for example, the sentence: "(...) a conjunction can actually be proven false just by knowing about the relation of its conjuncts and not necessary (sic) about their truth values." The page for disjunction literally has the sentence: "An operand of a disjunction is called a disjunct." – sgf Jul 8 '19 at 20:14
• Also, I think @MarsPlastic is right. Using conjunct and disjunct brings in the whole conceptual confusion that you get because a union actually conjoins the elements of the sets, but the union corresponds to the disjunction, etc. The equivalences are pretty straightforward, but at the same time very unintuitive. – sgf Jul 8 '19 at 20:16