In programing, you can always rewrite that first rule as "all" and "some" must compose over set union. So, "all (A ∪ B) == all A && all B", and "some (A ∪ B) == some A || some B".

That lets you discover the answer for the empty set.

As I think you would hope from a practical standpoint -- you don't want to have to handle a special case of false and always check if the array is empty.

I agree it's only logical in engineering contexts like that though, not in everyday language.

This is even what I expected, but I majored in math, so maybe that biased my response.

But if you consider “liar” to be an object,

> liar.hats.every((hat) => hat.color === "green")

will throw a TypeError: Cannot read properties of undefined. That’s definitely not `true`.