B Does Every Set in the Axiom of Choice Include an Empty Set?

[kidsasd987]

Following theorems are congruent(a) Axiom of Choice

(b) if ∀i:i∈I: <Yi | i∈I > → Yi≠Ø

(c) Ø∉S → ∃f: f is on a set S
s.t. f(X)∈X for all X∈S. where f is choice function of S.
I am confused with the theorem (c), as how the Collection S does not include empty set.
I believe every set needs to include an empty set as its element?

Can anyone please help me figure out this?

 

[TeethWhitener]

I believe every set needs to include an empty set as its element?

The empty set is a subset of every set, but not necessarily an element.