Intersection of two sets that contain other sets as elements How would the intersection of $A=\{a, b, e, \{a, b, c, d\}, \{d, e\}\}$ and $B=\{a, b, c, f, \{a, d\}, \{d, e\}\}$ be defined? I've searched quite a few books but no luck so far.

The intersection of two sets, say $A$ and $B$, is defined to be the set of elements in both $A$ and $B$. So if $A=\{1,2,3\}$ and $B=\{2,3,6,8\}$, then their intersection, denoted $A\cap B$ is
$$
A\cap B = \{2,3\}.
$$
Note that $2$ and $3$ are the only elements common to both $A$ and $B$.
Now, the only real difference for your particular $A$ and $B$ is that some of the elements are sets. Let's change our example. Say $A=\{1,2,\{3,4\}\}$ and $B=\{2,\{3,4\},\{6,8\}\}$. Note here that $\{3,4\}$ is an element of both $A$ and $B$. So $\{3,4\}$ is in their intersection. However, neither $3$ nor $4$ is an element of $A$ or $B$. Indeed, $3$ and $4$ are elements of the set $\{3,4\}$, which itself is an element of $A$ and $B$. So we see that
$$
A\cap B = \{2,\{3,4\}\}.
$$
See if you can identify the intersection of your sets, and feel free to ask if you need clarification.
