I have this two sets:
$A = \{\emptyset, \{\emptyset\}, \{\{\emptyset\}, \emptyset\}\}$
$B = \{\{x, \{x, y\}\} | x \in A, y \in A\}$
Now I want to list all possible elements that are in $B$. How do I do this?
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2$\begingroup$ Are you sure this is related to Mathematica and not to mathematics ? $\endgroup$– SektorCommented Oct 28, 2013 at 7:56
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2$\begingroup$ Pretty sure, since I want the program (Wolfram Mathematica, indeed) to list the possibilities for me ;) $\endgroup$– afpelCommented Oct 28, 2013 at 17:39
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1 Answer
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If I'm not mistaken you can do this: (I will replace [EmptySet] with ES because I have troubles formatting it here)
a = { ES, {ES}, {{ES}, ES}};
b = {#, {#, #2}} & @@@ Tuples[a, {2}];
% // Column
{ES, {ES, ES}} {ES, {ES, {ES}}} {ES, {ES, {{ES}, ES}}} {{ES}, {{ES}, ES}} {{ES}, {{ES}, {ES}}} {{ES}, {{ES}, {{ES}, ES}}} {{{ES}, ES}, {{{ES}, ES}, ES}} {{{ES}, ES}, {{{ES}, ES}, {ES}}} {{{ES}, ES}, {{{ES}, ES}, {{ES}, ES}}} }
Or even more clear way:
b2 = Table[{x, {x, y}}, {x, a}, {y, a}] // Flatten[#, 1] &;
b2 == b
True