Let $\Omega$ be the universal set (which contains all objects of interest) and let its complement be denoted by $\Omega^c$ . The book I'm reading states that $\Omega^c = \phi$ ; does that mean $\phi \not\subset \Omega$?
Let's make a community wiki answer based on the above comments.
Given the subset $A \subset \Omega$
The relative complement $A^c$ in $\Omega$ is defined as the set of elements of $\Omega$ that are not elements of $A$.
So in the case that $A = \Omega$, the relative complement of $A$ in $\Omega$ is equal to $\emptyset$.
That is, for every set $x$
we have $x \notin A^c$.
In particular we have $\emptyset \notin A^c$.
However, this is probably the "wrong" question to ask, because $\emptyset$ might not be an element of $\Omega$ at all.
Notice that the $\emptyset$ is a subset of every set, so in particular $\emptyset \subset \Omega$.
This is because to check whether $X \subset Y$ you take an arbitrary element of $X$ and check that it is also in $Y$. If $X$ is empty, then there is nothing to check.