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# Using the Logical iterative operator Exists to verify a SET in the domain

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Is it possible to use an indexed set inside the domain of Exists?

For instance:

1. I have an indexed set IS with index domain (a,b) and subset of c
2. I want to define a new set NS which is a subset of b and c
3. Is it possible to use in the definition of this new set NS the following expression:
{ (b,c) | Exists[ a | c in IS(a,b) ] }

Thank you

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Best answer by gdiepen 4 December 2023, 20:52

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Userlevel 5
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Instead of index sets, I typically try to use just binary parameters that indicate the relations instead.

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Thank you @gdiepen

Could you provide me an example or reference to understand what you are suggesting?

RM

Userlevel 5
+7

Instead of seeing the items as set elements, you can just define them as a relation using a binary parameter.

In your case you could create a binary parameter pIsPartOfIS(a,b,c) which gets a value 1 if c ‘is an element of the indexed set IS(a,b)’ and 0 otherwise.

Then your pIsPartOfNS(b,c) is just a new binary parameter with the definition exists(a | pIsPartOfIS(a,b,c)

Hope this is clear enough