Is it possible to express "any set B composed of any two elements from set A" using set theory notation? I have a set A with three elements. I'd like to express another set B in terms of a limited number of elements (two in this example) from set A.
In this case I realize that there would be a number of possible B sets, but I'm interested in expressing that B could be any of those sets.
Alternatively, set C which is one of the possible B sets.
Is this possible, or should I be looking for some other notation than set theory?
 A: If $A$ is a set and $n\in\Bbb N$, $[A]^n$ is a common notation for the set of $n$-element subsets of $A$. (In fact this notation is used more generally, with any cardinal $\kappa$, finite or infinite.) If you want the family of all $2$-element subsets of $A$, you can write $[A]^2$. If you want to say that $C$ is a member of that family: $C\in[A]^2$.
This notation is quite standard, but it’s not universally known, so you should probably define it the first time you use it.
Added: In case you find yourself wanting the subsets of $A$ having at most $n$ elements, you can write $[A]^{\le n}$; this is equally standard.
A: It's not uncommon to use binomial coefficients for this purpose:
$\tbinom{M}{c}=\{S\subseteq M\mid |S|=c\}$. The motivation fur this notation is that $\tbinom{|M|}{c}=\left| \tbinom{M}{c}\right|$. But, as you see in this answer, this notation isn't optimal for inline math. It's, however, quite common in graph theory (see https://mathoverflow.net/questions/36714/notation-for-a-graph-without-any-edges).
Another possibility is writing $\wp_c(M)$ for this set, as it is a subset of the power set. 
