True, correct. The universal set
U
is characterized by ∀:∈
∀
x
:
x
∈
U
. Taking the complement yields a set
U
c
that is characterized by ∀:∉
∀
x
:
x
∉
U
c
. This is equivalent to the statement ¬∃:∈
¬
∃
x
:
x
∈
U
c
and hence
U
c
is an (the) empty set. (Depending on your theory, there may not be a unique empty set.)
