alt Hacker NewsIn 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.
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.
Which leads to a funny fact that if all elements of the set S satisfy proposition P it doesn’t necessarily imply that some elements of the set S satisfy proposition P.