First of all, I had no idea what to title this question, so feel free to change it to something more appropriate.
I have a set defined as such:
$\{a\frown b\mid a \in A \wedge b \in \{c\frown d\mid c \in C \wedge d \in D\}\}$
Is that logically equivalent to:
$\{a\frown (c\frown d)\mid a \in A \wedge c \in C \wedge d \in D\}$
Assuming that $\frown$ is an associative relation.