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I would like to define a map (a "multiplication" denoted $\otimes$) over the finite set of symbols $G=\{a,b,c,d,e,f,g,h\}$. I would like to define several rules like $$a \otimes b= \{b \} $$ $$a \otimes h= \{h,g\} $$

etc. So the mapping is from $G \times G$ to the power set of G (i.e, to the set of all subsets of G). Can someone kindly suggest some ways as to define such an abstract system of labels, and the above map?

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  • $\begingroup$ a\[TensorProduct]h = {h, g}? $\endgroup$ – AccidentalFourierTransform Jul 7 '18 at 14:53
  • $\begingroup$ @AccidentalFourierTransform Yes. Tensor product is just a symbol that I am using for the map $\otimes: G \times G \rightarrow P(G) $ where P(G) denotes the power set of G. $\endgroup$ – Rajath Krishna R Jul 7 '18 at 14:55

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