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'Five girls and boys'

I wonder what the denotation and type is of the disjunction 'or' in this phrase. I have 'five' as type <e,t><e,t>t> and the denotation as λPλQ[|P ∩ Q|= 10], but I am unsure what the denotation of the 'or' would be.

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    'or' does not appear in the example. 'and', however, does. In this context, 'and' seems to have a somewhat disjunctive sense to it, since 'five girls and boys' means 'five individuals each of which is a girl or a boy'. – Gregory Nisbet Apr 14 at 0:45
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It depends on what the sentence is supposed to mean:

  1. Either five girls run or five boys run
  2. Five individuals run, each of whom is either a girl or a boy

To my intuition, 2. is the more plausible one. Under this reading, the quantifier restriction (the P part) consists of mixing some girls and boys together. This amounts to forming the union of the set of girls and the set of boys. So eventually one would want to end up with

|(G ∪ B) ∩ R| = 5

So if the semantics of "or" in this context is to combine with "girls" and "boys" and return their union, can you figure out how it must be defined?

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