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I would like to denote the following set:

$$ \bigl\{\{a,b\}:a\in A\text{ and }b\in B\bigr\} $$

I have found this (Notation for unordered product of sets) but I do not know how this is answer my question. The answer says to use the notation $\binom{V}{2}$ but I have two sets $A$ and $B$ not only one $V$.

Thanks.

Community
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Chiba
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1 Answers1

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Assuming that $A$ is disjoint from $B$, you could denote this as:

$$\left\{\{a,b\}~:~a\in A,b\in B\right\}=\binom{A\cup B}{2}\setminus \left(\binom{A}{2}\cup \binom{B}{2}\right)$$

I.e. the family of all subsets of size two of $A\cup B$ such that the elements are neither both from $A$ nor are both from $B$, using the notation that $\binom{X}{2} = \{E~:~E\subseteq X,~|E|=2\}$, the family of all subsets of size two of $X$.

Beyond that, this is not commonly used and I know of no symbol to denote this. Creating your own symbol to use so long as you define it in any paper you use it in for the reader is fine, or you can simply skip using a symbol altogether and just write it as the set in the way you already did in your question.

JMoravitz
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  • If you wish to fix the above for use with sets that are not necessarily disjoint, you could try playing with unioning the above with things like $\binom{A}{2}\setminus \binom{A\setminus B}{2}$ to add back in the pairs which were accidentally removed. – JMoravitz Feb 15 '16 at 03:35