I'm struggling for the correct vocabulary/notation for the following situation. Let's say S
is a (very simple) set with the following composition:
S = {1, 2, 3, 4, 5, 6}
Now, there are two subsets which compose this set, A
and B
:
A = {1, 2}
B = {3, 4, 5, 6}
Obviously, A is a subset of S, $A \subseteq S$, and B is a subset of S, $B \subseteq S$.
Not only are A and B subsets of S, these are subsets which uniquely compose S, i.e.
$A \cup B = S$ and $A \cap B = \varnothing$
(1) What is the vocabulary used to describe these type of subsets? A "unique" subset?
(2) If there is no special terminology, how would one best convey this concept notationally?
e.g.
$A \subseteq S$ and $B \subseteq S$ s.t. $A \cap B = \varnothing$
maybe be one possibility, but it doesn't show that the union of A and B are the set S...