This is an excellent example of the very common educational method that I call "Say something
foggy, explain nothing, see the kids going nuts and go and drink a beer in full satisfaction" .
In this case the issue is far from being standard in mathematics and different people may have
different views, though I think that many (most?) people will agree with the book you're working with:
1) if we take the intersection over an (the, in fact) empty subset of , then
we can think of this as the set of all the elements that belong to all and each
of the elements (subsets of ) that appear in that intersection...but there are no
sets at all there, so we can argue that ANY element in appears there under the
logical argument "show me one subset that appears in that intersection and I'll prove you that any
element of the set is contained there"...
2) Something simmilar happens with the union of the empty family on : if
there exists an element in that union then some of the subsets there contains it...but there are no
subsets there so the union is the empty set.
Yeah, I know...not the most brilliant moment in mathematics foundations (set theory and stuff), but
if you agree with those conveniences then there's no problem.
I, for one, would never say such a thing without first trying to explain a little all this madness, and
even less would I claim that we can drop (1) because so and so, as if it were an obvious fact.