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Given two sets $ A = \{\{1\} , \{2 , 6\} \}$ and $ B = \{\{2\} , \{3\} , \{4 , 5\} \}$, what set operation can produce $$ C = \{ \{ 1 , 2 \} , \{ 1 , 3 \} , \{ 1 , 4 , 5 \} , \{ 2 , 6 , 2 \} , \{ 2 , 6 , 3 \} , \{ 2 , 6 , 4 , 5 \}\}? $$

The set $ C $ is gained by Cartesian product firstly, then two elements of each pair are combined by union. I wonder whether there is a more simple solution?

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    $\begingroup$ I’d describe $C$ simply as $\{a\cup b:a\in A\land b\in B\}$, which is of course equivalent to your $\{a\cup b:\langle a,b\rangle\in A\times B\}$. I see nothing simpler. $\endgroup$ – Brian M. Scott Apr 1 '12 at 21:44
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    $\begingroup$ If were allowed to make up names, I call it "Cartesian union"! $\endgroup$ – user2468 Apr 1 '12 at 23:32
  • $\begingroup$ Thanks a lot, Brain M. Scott and J.D.. Why not Kejia Union :-D $\endgroup$ – 象嘉道 Apr 2 '12 at 17:10
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Converting comment to answer to get this off the Unanswered list:

I’d describe $C$ simply as $\{a\cup b:a\in A\land b\in B\}$, which is of course equivalent to your $\{a\cup b:\langle a,b\rangle \in A\times B\}$. I see nothing simpler.

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