MHB Finding a Cayley Table for a Groupoid: an Example

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Hey! :o

Could you give me a hint how we can find the Cayley table of a groupoid?

For example for the groupoid $(2^{\{a,b\}},\setminus )\times (\{0,1\},\min )$. (Wondering) ( $\setminus$ means the set difference )
 
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mathmari said:
For example for the groupoid $(2^{\{a,b\}},\setminus )\times (\{0,1\},\min )$.
Why can't you write it by definition?
 
Evgeny.Makarov said:
Why can't you write it by definition?

What do you mean? (Wondering)
 
You have the definition of Cayley table: at the intersection of row $x$ and column $y$ you write the result of the operation on $x$ and $y$. You also have the definition of the operation. What prevents you from filling the table?
 

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