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To elaborate on this point, "if you score 90 and above" could be parsed in two different ways:

  1. "if [you score 90] and [you score above 90]"
  2. "if you score in [{90} 'and' {x: x > 90}]"
[1] is unsatisfiable. [2] is still ambiguous, as it's unclear in natural language whether 'and' is a set union or intersection.

In mathematical terminology, 'and' in this countext would mean set intersection, but I don't think it's necessarily "incorrect" to have this mean set union in natural language.

To elaborate, take: C = A union B. Here are two propositions about C:

  I. forall c in C. (c in A) OR (c in B)
  II. (forall a in A. a in C) AND (forall b in B. b in C)
These propositions are not equivalent. [I] actually implies C is a subset of (A union B), and [II] implies that it's a superset. Note that set builder notation for C, {c: (c in A) OR (c in B)} is structurally very similar to [I].

I think [II] is the interpretation of 'and' that is intended through the natural language use. It's essentially a form of set construction: I am constructing a set; it contains 90, and it contains the numbers above 90. As a set construction it also adds an implicit constraint that the new set can't contain anything not in the operands, so that resolves the superset ambiguity (it would be patently absurd in natural language to claim that 55 could be in the set "90 and above").




I don't read it that way. To me the use of the word "AND" is a red herring, as it wasn't meant to imply a logical operation, but rather in the usual sense (and meaning "plus that") to denote the range as half open.

  [90, infinity)
as opposed to:

  (90, infinity)
https://en.wikipedia.org/wiki/Interval_%28mathematics%29#Inc...


The ACTUAL meaning:

3. "if [you score 90] do [x] and if you score [above 90] also do [x]"




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