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I have an expression of set unions and intersections, but one or more sets are unknown.
An easy example (X is the unknown set):
$S = (A \cap X) \cup B$.
I am searching for an algorithm to give me the smallest known superset of S given the expression above.
In this case the answer would be $A \cup B$.
More examples: (U is the "set of everything")
$A \cup X$ -> U
$A \cap X$ -> A
$(A \cap X)^C$ -> U
$((A \cap X) \cup B)^C$ -> $B^C$

Apologies if this is rather a question for stackoverflow, in that case let me know.

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  • $\begingroup$ given S(X), is the answer S(X = {}) U S(X = U)? i assume that the answer resides at one of both extrema of possible X, either empty set or U. $\endgroup$
    – nnolte
    Apr 16, 2020 at 11:22
  • $\begingroup$ actually i don't think this is true, need to find a counter-example $\endgroup$
    – nnolte
    Apr 16, 2020 at 11:29

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