Which is the notation for grouping elements from two sets two by two? We can unite two sets $A=\{a,b\}$ and $B=\{c\}$, by saying $C = A \cup B = \{a,b,c\}$. And we can perform a cartesian product like this:
$C = A \times B = \{\langle a,c \rangle, \langle b,c\rangle\}$
How can I represent the following set operation? Which symbol could be used in the place of '?'?
$$C = A ~?~ B = \{\{a,c\}, \{b,c\}\}$$
It is like the cartesian product, but resulting in a set of sets of size 2, instead of a set of pairs (tuples).
 A: There is no standard notation for this. Probably the best thing to use is set-builder notation:
$$
C = \{ \{x, y\} : x \in A, y \in B \}.
$$
This will also allow for singletons. For example, if you would take $A = \{a,b,c\}$ and $B = \{c\}$, then you would get $\{c\} \in C$ (since $c$ is in both $A$ and $B$). If you do not want that, you can use
$$
C = \{ \{x, y\} : x \in A, y \in B, x \neq y \}.
$$
A: Don't know that there is one.
But if you want to formally defined such a set you can invent any notation you like and define:
$A?B = \{\{a,b\}|a\in A; b\in B\}$
Actually more to the point is the a symbol or function that we "unorder" an ordered tuple?  Something akin to $<a_1, ....., a_k>_u = \{a_1, ...., a_k\}$.  
We can define such a function as $u: A\times B \to   \mathscr P(A\cup B)$ via $u(<a,b>) = \{a,b\}$ and then then set you want can be defined as $u(A\times B)$.
I don't know if there is a convention for the concept but.... you can certainly define what you need.
But thing is the only difference between $\{a,b\}$ and $<a,b>$ is a specified order. So many would simply call this an "unordered pair".
