# the empty set question (member of/subsets)

I'm trying to find a counterexample to this statement: "If $A \in B$ and $B \subseteq C$, then $A \in C$."

So I thought I could use $\emptyset$.

Is the empty set a member of a set containing the empty set?

So, if $A = \emptyset$ and $B = \{\emptyset\}$ is $A \in B$?

• The empty set is a subset of any set. Your statement is actually a true one. – The Count Feb 7 '17 at 21:45

Sure $\emptyset \in \{\emptyset\}$, it's the only member, in fact.
BTW, you wont't find a counterexample to the claim. $B \subseteq C$ is defined as "every member of $B$ is a member of $C$".