5
$\begingroup$

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?

  • 0
    Thanks a lot, Brain M. Scott and J.D.. Why not **Kejia Union** :-D – 2012-04-02

1 Answers 1

4

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.

  • 0
    @Brain M.Scott: Could you help me out this question: http://math.stackexchange.com/questions/416052/let-x-be-a-moore-space-and-ex-omega-is-it-metrizable – 2013-06-10