Hi

Here's a problem from Enderton's set theory book (1977) page 39.

"Assume that A and B are given sets and show that there exists a set C such that

for any y

$\displaystyle y\in C\Leftrightarrow \exists x \in A(y=\{x\}\times B)$

In other words, show that $\displaystyle \{\{x\}\times B\lvert x\in A\}$ is a set "

since this is an existence statement, I am unsure as to how to cook up C.

can anybody give some direction ?