Finding a Cayley Table for a Groupoid: an Example

[mathmari]

Hey!

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 )

 

[Evgeny.Makarov]

For example for the groupoid $(2^{\{a,b\}},\setminus )\times (\{0,1\},\min )$.

Why can't you write it by definition?

 

[mathmari]

Why can't you write it by definition?

What do you mean? (Wondering)

 

[Evgeny.Makarov]

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?